Luxembourg - Math Olympiad Question | You should know this trick

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  • Опубліковано 29 лис 2024
  • Maths Olympiads are held all around the world to recognise students who excel in maths. The test is offered at many grade levels and provides them with numerous possibilities to win certifications, awards, and even scholarships for higher studies.

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  • @RickDesper-v8z
    @RickDesper-v8z Рік тому +203

    Instead of looking for (a-b)^2 = 3 - 2 sqrt(2), I looked for (a + b sqrt(2))^2 = (3 - 2 sqrt(2)), with a, b rational numbers. The advantage here is that I don't have to pull a and b out of thin air: I can solve for them.
    In this case we have a^2 + 2 b^2 = 3 and 2ab = -2. There are two solutions here: a = -1, b = 1, and a = 1, b = -1. The latter choice is the positive result implied by the radical. So the answer is -1 + sqrt(2).
    How did I know to look for an answer in this form? From more advanced math, I know that Q[sqrt(2)] is a field, which means specifically for us that it's closed under multiplication. So it's a good place to start when looking for roots of a polynomial.

    • @NazriB
      @NazriB Рік тому

      Lies again? Must See TV Deaf Blind

    • @yu-yu704
      @yu-yu704 Рік тому +3

      I remember seeing this trick of manipulation of sqrt(2) like imaginary numbers, but I didn’t realize it had a formal name Q(sqrt(2))

    • @RozoClopero-hj9lf
      @RozoClopero-hj9lf Рік тому

      You can also use the fact that for a = sqrt(3 - sqrt(8)) and b = sqrt(3 + sqrt(8)) we find that ab = 1 and a + b = sqrt(8), hence x^2 - sqrt(8)x + 1 = 0 have - 1 + sqrt(2) and 1 + sqrt(2) for solution.

    • @johnklaus9111
      @johnklaus9111 6 місяців тому +1

      So -1 is on of your answers for a square root problem? What times what equals negative 1?
      Ooops...

    • @emankhan6094
      @emankhan6094 5 місяців тому

      2+2= 4

  • @georgevisvikis1878
    @georgevisvikis1878 Рік тому +2031

    It is too simple for Math-Olympiad.

    • @vishal.gupta1
      @vishal.gupta1 Рік тому +66

      Agreed

    • @oficialmundodiverso
      @oficialmundodiverso Рік тому +50

      No

    • @uwuowo7775
      @uwuowo7775 Рік тому +148

      ​@@furina9053Olympiad math is just a whole different level man, thats why they mentioned it

    • @volkanatar4232
      @volkanatar4232 Рік тому +135

      I think it was maybe paralympic games

    • @SkyBlue0
      @SkyBlue0 Рік тому +32

      Maybe it was from the qualifier level exam

  • @pdas6145
    @pdas6145 Рік тому +63

    One should be careful in distinguishing between 'equals' and 'implies' symbols.

  • @DrKleinIll
    @DrKleinIll Рік тому +37

    People commenting it is too simple are unrecognized genius. I wonder why they are wasting their time watching youtube videos. I mean, it is not the hardest question, but it does takes more thinking than a regular polynomial question and corresponds to high school students level

    • @dhonikumarshahi2806
      @dhonikumarshahi2806 2 місяці тому +4

      Skill issue 😂

    • @fahimfuad92
      @fahimfuad92 2 місяці тому

      Ha ha
      So funny man.
      You probably should become a standing comedian​@@dhonikumarshahi2806

    • @alexp2019
      @alexp2019 Місяць тому +4

      Is it high school level?😂 not 8th grade?

    • @archmaneric9251
      @archmaneric9251 Місяць тому +1

      Im not a genius and I solved it in my head lying in bed in about 60 seconds. It's too simple

    • @DOROHEDOROFAN
      @DOROHEDOROFAN 25 днів тому

      @@archmaneric9251 sarcasm

  • @jim2376
    @jim2376 Рік тому +172

    √(3 - 2√2). Shortcut: 2 + 1 = 3 and 2 x 1 = 2. Automatic: √2 - √1 which simplifies to √2 - 1. Use the shortcut and don't overthink it.

    • @killanxv
      @killanxv Рік тому +16

      i didn't get your point

    • @jim2376
      @jim2376 Рік тому +17

      @@killanxv If (1) the coefficient in front of the second term is 2, and (2) the numbers summing to the first term are the same as factors multiplying to the radicand in the second term, then the answer is the sum or difference of the roots of the two numbers summing to the first term. See my post above. Gotta have that coefficient of 2 in front of the radical sign in the second term. √(15 + √200)) √200 = √(4 x 50) = 2√50. Bingo! Got the coefficient of 2. Now 10 + 5 = 15 and 10 x 5 = 50. Throw radical signs over 10 and 5 for your answer: √10 + √5. Note that we keep the sign in the original problem. Hope this helps.

    • @abhishekchhikara4100
      @abhishekchhikara4100 Рік тому +15

      ​@@jim2376made even more difficult 😂 , what is a radicand ? Too simple earlier , it happens by simple instincts

    • @SunnyRosy-uk1ch
      @SunnyRosy-uk1ch Рік тому +8

      ​@@abhishekchhikara4100That's for people like you, just go and read definitions and you can see the word radicand is so common in most textbooks

    • @James_Lindgaard
      @James_Lindgaard Рік тому

      What happens when your teacher wants to see the problem worked step by step?

  • @stephenbennett1127
    @stephenbennett1127 Рік тому +192

    I am a genuine maths dunce. Don't remember learning any of this and I don't understand it now either! 😅

  • @forestfairy4025
    @forestfairy4025 11 місяців тому +35

    I hope one day everyone finds the peace in math! Love from Türkiye.

    • @ibrahimhalilalpaslan1259
      @ibrahimhalilalpaslan1259 11 місяців тому +2

      Well we are not going to find it until we get fair question remember differential problem in 2021? İ dont know if youre university preparing student or you did but just check it out

    • @albertdumont4977
      @albertdumont4977 Місяць тому +2

      A japanese guy once told me something that changed my life. He said that the common people's mind makes a very assertive division between leisure and studies. The secret is to look at exercises like puzzles or games, in such a way that you don't see youself as studing, but having fun instead. That's why nerds never get tired of studies, they can't stop indeed. I know its sounds crazy, but beleive me, it works very well, mainly im mathematics.

  • @keithapps
    @keithapps Рік тому +78

    When I went to a secondary modern senior school in 1958 I was taught to be literate and numerate, I worked as a precision engineer but I don't have a clue what the lady is talking about.

    • @anilthomas5658
      @anilthomas5658 8 місяців тому +2

      Bro this for real made me fall of my bed laughin

    • @yomyomcam
      @yomyomcam 8 місяців тому +2

      She got this "trick" out of a Deus Ex Machina

  • @pawedziedzic3250
    @pawedziedzic3250 Рік тому +18

    People saying this is too simple, and while it kind of is simple, it is also hard to come up with unless you are trained to apply this kind of thinking in problems. I would have never guessed to use the square of difference identity, feels like its a problem you have to be familiar with beforehand

    • @Aman-nk5uq
      @Aman-nk5uq Рік тому +3

      Yupp, one must have known the patterns before

    • @novaastronomia8720
      @novaastronomia8720 11 місяців тому +1

      I think its not that hard. In √(3-2√2), the 3-2√2 is inside a sq root, which makes us try forms like (a±b)^2

    • @Ispeakwithlogic
      @Ispeakwithlogic 8 місяців тому +2

      It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡

    • @mar2506
      @mar2506 7 місяців тому

      "it is also hard to come up with unless you are trained to apply this kind of thinking in problems"
      .
      those who are spesicically trained for olympiands, will be trained for this and much more , becomes it too easy for them.

    • @RavinderKumarSharma-pw9ke
      @RavinderKumarSharma-pw9ke 3 місяці тому

      ​@mar2506 an averag 8th grader from India will be able to this in seconds brh.
      U'll find this in cbse books

  • @ShereenSultana-nf6if
    @ShereenSultana-nf6if 6 місяців тому +3

    To solve the given expression, we can simplify it step by step:
    Simplify the square root of 9: v9=3
    Simplify the square root of 8: v8=2v2
    Substitute the simplified values back into the original expression: v3-2v2
    Therefore, the solution to the given expression is v3-2v2

  • @MrAustrianoak
    @MrAustrianoak Рік тому +60

    Because in the main question the number under square root is definitely positive, as squared root of 9 is bigger than squared root of 8.

    • @scottrichmond3548
      @scottrichmond3548 Рік тому +4

      Then again, the square root of 9 is also -3, so there are two answers.

    • @rudraroopbhattacharjee6191
      @rudraroopbhattacharjee6191 Рік тому +8

      @@scottrichmond3548 square root of 9 is 3 not -3

    • @antronx7
      @antronx7 Рік тому +1

      @@rudraroopbhattacharjee6191 what's -3 * -3 ?

    • @rudraroopbhattacharjee6191
      @rudraroopbhattacharjee6191 Рік тому +1

      @@antronx7 9

    • @rudraroopbhattacharjee6191
      @rudraroopbhattacharjee6191 Рік тому +7

      @@antronx7 I understand what you are trying to say but its a rule of mathematics that in Real numbers, √x is always non negative.
      What you mean to say is-
      Roots of X² are ±√(x²)
      See, the ± comes before a square root thing. This is because a square root can never be negative.
      In your case,
      X² = 9
      X = ±√9
      X = +3, -3

  • @davidbrisbane7206
    @davidbrisbane7206 Рік тому +23

    Now √(√9 - √8) = √(3 - 2√2).
    Now suppose √(√3 - 2√2) = a + b√2, where a and b are integers. This maybe not actually have a solution in integers, but if it does, we can find them as follows.
    Let 3 - 2√2 = (a + b√2)²
    = (a² + 2b²) + 2ab√2
    So, 3 = a² + 2b² and -2 = 2ab
    So, (a = 1 and b = -1) or (a = -1 and b = 1).
    However, a + b√2 ≥ 0, as otherwise √(√9 - √8) would be a complex number, so we are forced to conclude that a = -1 and b = 1 is the only possible solution.
    So, √(√9 - √8) = -1 + 1*√2 = √2 - 1.

    • @samarthsamrat8378
      @samarthsamrat8378 Рік тому +1

      It can be the other method which is great but the standard one is more easy and convinnient

    • @RickDesper-v8z
      @RickDesper-v8z Рік тому +2

      I'd start by relaxing to let a, b be rational numbers. Then be pleasantly surprised when they turn out to be integers. The rest of the process is exactly the same.

  • @parasuraman1155
    @parasuraman1155 Рік тому +125

    Appreciate that there are some Maths Olympiad questions within our grasp.
    I forgot the sqrt(square) trick from high school, but would have been able to do it then.
    These are like IIT JEE questions, maybe training questions, those students would argue.
    I expect IIT JEE students (even students) to call this easy by IIT JEE standard.
    Which would make me average in Maths. At 90 percentile in Quantitative Ability in the Stamford-Binet V test.

    • @eddie31415
      @eddie31415 Рік тому +2

      yeah, it's an easy question. Like JEE Mains level probably.

    • @Kanuos-xd8ej
      @Kanuos-xd8ej Рік тому

      @@eddie31415 this is class 9 school level.

    • @srivatsnaman
      @srivatsnaman Рік тому +13

      This question is in Class 9 R D Sharma Factorisation of Polynomials fill in the blanks in the form of √3 -2√2.

    • @blank3580
      @blank3580 Рік тому +8

      @@eddie31415 lol no 8th or 9th class problem maybe jee mains level are far more harder than thiss

    • @NaplesFC
      @NaplesFC Рік тому +1

      @@eddie31415 it's a grade 9th or 10th question maybe

  • @praveendavuluri9576
    @praveendavuluri9576 Рік тому +4

    Why do you need ( a-b)(a-b)? You can simply find the answer at 3-2√2 only na. 3-2*1.414=3-2.828=.172=√.172=.414 which is the same one.

    • @lesouni9342
      @lesouni9342 8 місяців тому +1

      Im guessing you're not allowed a calculator in this exam , as such your calculation are only approximation and can't be used as answers.

    • @praveendavuluri9576
      @praveendavuluri9576 8 місяців тому +1

      @@lesouni9342 you don't need a calculator for such easy things.you don't even need a pen& paper for sure.

    • @emankhan6094
      @emankhan6094 5 місяців тому

      2+8= 10

    • @emankhan6094
      @emankhan6094 5 місяців тому

      Hiding qusoin are

  • @EngineeringTR
    @EngineeringTR Рік тому +9

    There is a rule if it is in the form of sqrt(sqrt(x+y)-2sqrt(x.y)) then the result is sqrt(x)-sqrt(y). For this question sqrt(sqrt(2+1)-2[sqrt(2)*sqrt(1)])=sqrt(2)-sqrt(1)=sqrt(2)-1

    • @atulyaroy8962
      @atulyaroy8962 Рік тому

      Well it's better to be said identity, since it holds for all Reals. Like a process has a rule to (for example) integrate by parts, you assume 1 function to be 1st and other to be second then you apply the formula of rule. Just my take.

    • @RickDesper-v8z
      @RickDesper-v8z Рік тому

      This doesn't look exactly right. Square your RHS. You get (x + y) - 2 sqrt(xy). You need to lose one "sqrt" on the left hand side. To wit: sqrt((x + y) - 2 sqrt(xy)) = +/- (sqrt(x) - sqrt(y)), with the sign chosen on the RHS to ensure the number is positive.

  • @luanh8125
    @luanh8125 Рік тому +305

    We were solving such problems in my 8th grade in Romania in a regular maths class. Too simple for an Olympiad.

    • @jonavuka
      @jonavuka Рік тому +62

      no one cares

    • @thomasjefferson6225
      @thomasjefferson6225 Рік тому

      I'm sure third world Romania isn't.

    • @GeorgeRoussas
      @GeorgeRoussas Рік тому +1

      I wonder if no baddy needs mathema😊ticks why still teach them

    • @Mayhamsdead
      @Mayhamsdead Рік тому +1

      Cope and seethe.

    • @Mayhamsdead
      @Mayhamsdead Рік тому +20

      China and Romania have always been at the top when in comes to math, but I don't necessarily think the method used to achieve that goal was a positive one.

  • @AlexandreSNunes
    @AlexandreSNunes Рік тому +123

    As a martian, I teached myself this trick at 6 months old, by observing shadow patterns in our red planet.

    • @jassaljs
      @jassaljs Рік тому +5

      😂

    • @Dad_Of_Atreus
      @Dad_Of_Atreus 8 місяців тому +2

      Ain't no martian looks like a mongoose 🗣️

    • @albertdumont4977
      @albertdumont4977 Місяць тому +1

      Don't let Elon Musk colonize Mars. What a pity if the red planet becoming stupid as Earth.

  • @rizbuild
    @rizbuild Місяць тому

    Solved by AI
    √9-√8=?
    To evaluate the expression √9 - √8, we need to simplify the square roots.
    √9 = √(3²) = 3 (since 3² = 9)
    √8 = √(2² × 2) = 2√2 (since 2² × 2 = 8)
    Now, subtract:
    3 - 2√2
    To simplify further, we can approximate 2√2 as 2.83.
    3 - 2.83 = 0.17
    So, √9 - √8 ≈ 0.17.

  • @UNKNOWNPERSON-kk9kd
    @UNKNOWNPERSON-kk9kd Рік тому +21

    Nicely done and thank you.
    However, I'll just use my handy electronic calculator for these kind of problems.

  • @dailyhealthmotivation7079
    @dailyhealthmotivation7079 Місяць тому +1

    It's simple
    Question for Vedic Mathematics
    =√3-2.8286
    =√0.1714
    *=0.414*

  • @MateFast_Oficial
    @MateFast_Oficial Рік тому +28

    Para los que piden solución negativa, recuerden que:
    x^2=4
    no es lo mismo que
    x=√4
    ....

    • @davidecampana269
      @davidecampana269 Рік тому

      Esatto. Dai che a novembre quando non sarò più quello dei numeri e tiferò Putin che farà un bel botto nucleare vi regalerò giubbotti di plastica a specchio, piscine in muratura e motomacchine che sfrecciano a 500 orari. Da novembre ci divertiamo tutti contro tutti col finale nucleare planetario

    • @plutao_pt
      @plutao_pt Рік тому

      pero cuadrados negatvos no existen

    • @emankhan6094
      @emankhan6094 5 місяців тому

      2+2 =4

    • @emankhan6094
      @emankhan6094 5 місяців тому

      4+4 = 8

  • @SiddharthGautam-ry5wt
    @SiddharthGautam-ry5wt 10 місяців тому

    Real Olympiad questions
    Let a and b be positive integers such that ab+1 divides a²+b². Show that a²+b²/ab+1 is the square of an integer.

  • @George-Toby
    @George-Toby Рік тому +11

    I knew this ...i just forget about it. That's what happens when you don't stay in practice

    • @tomcherry1976
      @tomcherry1976 Рік тому +1

      Ashole cleaning in Hospital useless.

  • @akosmagyar4878
    @akosmagyar4878 Рік тому +1

    This is a standard problem. You reduce it to sqrt (sqrt (9)+sqrt(8))=sqrt (2+2\sqrt(2)+1)=sqrt(2)+1.

  • @NainsiArya1818
    @NainsiArya1818 5 місяців тому +30

    Being an IIT - JEE aspirant from India , It is one of the easiest category of maths problem I ever met !

    • @mathematicsman7454
      @mathematicsman7454 4 місяці тому

      I know the trick too.... But if anybody don't know the trick of solving it directly....they too have to give a minute..... Professor of college who are doing PhD in mathematics don't know such trick and they may take a minute to solve it's doesn't mean that they know less math than you okay...... I hope you otherstand the difference

    • @NainsiArya1818
      @NainsiArya1818 4 місяці тому +3

      @@mathematicsman7454 I am not judging anyone as If someone is able to solve this problem she may be genius and the one who isn't is weak in maths . I was just saying that even in Maths Olympiad , there comes questions which can be solved just by basics ! Well I respect your opinion ..

    • @CuRiOuS--MEHRAN
      @CuRiOuS--MEHRAN 3 місяці тому

      Thankyou for being my competition

    • @deepamurthy198
      @deepamurthy198 3 місяці тому +1

      And in IIT JEE we never got such questions

    • @NainsiArya1818
      @NainsiArya1818 3 місяці тому

      @@deepamurthy198 Yah !

  • @bharatiyagamerg
    @bharatiyagamerg 3 місяці тому +1

    To simple 🙃
    √( √9 - √8)
    √( 3 - √8)
    √( 3 - 2×1.41)
    √( 3 - 2.82)
    √( .18 ) => near to √16
    So as my own formula 😂 ( work only when number are near to root )
    Information √.16=> .4
    √.18
    .4 + 1/18
    => .4 + .056
    => .456 (it is approx without so much calculations 😅)
    Well the 1/18 , its come from my formula
    Like if someone root value are near to square
    √24 = √25 - (25-24)/( *2* * 25)
    *2* is constant 😊

  • @rupakdey2803
    @rupakdey2803 Рік тому +3

    To solve the problem here, two symbols used ie. "Is equal to" and "implies". For simplification "is equal to" is used. But to solve an equation "implies" symble is used.

    • @bluebow9347
      @bluebow9347 7 місяців тому

      Can you specify the implies symbol?

  • @mokhtarali8749
    @mokhtarali8749 2 місяці тому

    2V2=2ab =2×1×V2>>1×V2 (a=1 ,b=V2 or a=V2 ,b=1)

  • @nguyenquoccuong3311
    @nguyenquoccuong3311 Рік тому +11

    it's for secondary school in Vietnam 😂

    • @hoangdj
      @hoangdj Рік тому +2

      True story 😂

  • @albertdumont4977
    @albertdumont4977 Місяць тому +1

    Thank you girl, from the buttom of my heart. I nearly end up in the asylum trying to solve exercises like this. Besides a great mathematician you also have psyquiatric talents.

  • @davidanderson5310
    @davidanderson5310 Рік тому +3

    What's the motivation for trying to express it as a^2 - 2ab + b^2? If you don't already know the answer, why would you do that?

    • @OptimusCrime4444
      @OptimusCrime4444 Рік тому

      This method is called compleating the square. You map your current problem on the binomial formula and then use it to simplify the problem. Which she did.
      I did not watch the video with sound on. Not sure why everyone is so negative in the comments...

    • @Ispeakwithlogic
      @Ispeakwithlogic 8 місяців тому

      It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡

  • @Crazy_mathematics
    @Crazy_mathematics Рік тому

    √(√9+√8) =√(3+√8) = √x + √y
    Then,
    x+y =3
    x-y=1 √2 + √1
    *Get it from Carr's synopsis ( book used by ramanujan to self study)

  • @seamoreplant
    @seamoreplant Рік тому +13

    I could have gone my whole life without knowing that answer! Now I know!

    • @glasssmirror2314
      @glasssmirror2314 9 місяців тому

      Please help me to solve using diff of 2 sq as mentioned by teacher but not followed.

  • @liralira8710
    @liralira8710 Рік тому

    Equation with double radical The first number will be added to the second. And then it's going to be the product of the first number and the second.
    ✓3-2√2= S=2+1=3. P=2.(-1)=-2. ✓2-1 .

  • @freddyalvaradamaranon304
    @freddyalvaradamaranon304 Рік тому +9

    Interesante y didáctica explicación, muchas gracias por compartir 😊❤😊

  • @serioustourist2574
    @serioustourist2574 2 місяці тому +1

    3-2✓2 = 3-2*1.414 just product and subtract will give your answer

  • @allenmurray7893
    @allenmurray7893 Рік тому +10

    I am totally lost from the start.

  • @gzannos
    @gzannos Рік тому +1

    Since Sq root of 2 -1 is positive you don't have to use absolute value

  • @pavelkovarik144
    @pavelkovarik144 Рік тому +41

    Used calculator, got same result.💪

    • @Bananajoe474
      @Bananajoe474 9 місяців тому +3

      Work smarter not harder 💪

  • @artavazd0
    @artavazd0 Місяць тому

    Задача имеет 8 решений---------- +-(корень из 2 +1), +-(корень из 2 - 1), +-i(корень из 2 +1), +-i(корень из 2 - 1).

  • @volodymyrtsurko
    @volodymyrtsurko Рік тому +17

    I do not know how much time it would take for me until realizing that 3 - 2sqrt(2) can be easily presented in a form of a^2 - 2ab + b^2. Do mathematicians have a special ability to glance it on the spot when something can be recombined according to the known rule?

    • @TheMeiravital
      @TheMeiravital Рік тому +6

      I think it is more about having experience and mastery with those tools. In many schools we skip to differentials and integrals before having a solid grasp on foundations of math. It's like they think mathematics was an intellectual desert up until newton and Leibniz. If students are educated to maximize their mathematical tools before learning new ones, they'd know how to solve these problems. (The Israeli school system is worse than the american, we don't even learn completing the square, so we'd have no intuition for solving this kind of problem)

    • @Jxsh_Lofi
      @Jxsh_Lofi Рік тому

      ​@@TheMeiravital😂

    • @Kandralla
      @Kandralla Рік тому +4

      ​@@TheMeiravital Thank God they did do that otherwise I would have failed math. Memorizing patterns is not as useful as understanding why. ESPECIALLY once you realize that in the real world math never works out nicely like that.

    • @mnlight8308
      @mnlight8308 Рік тому

      I thought I was the only one who had this shitty problem, I had to solve advanced math problems without having enough time to fully memorize algebra formulas due to lockdown. And now everyone is kicking ass

    • @ArchangelAurora
      @ArchangelAurora Рік тому +1

      I think they just saw the same or very similar solutions over and over. I asked my math professor a question before and he solved it by adding 1 to the both sides of the equation. When I asked why would he do something weird like that and he told me that they just get used to this patterns over the years.

  • @kushagravarshney7683
    @kushagravarshney7683 Рік тому +1

    Instead of doing this simply let the whole thing be x and form a quadritic equation and just solve it. Isn't it better to give all the possible values rather than just 1 value?

  • @thefuturist8864
    @thefuturist8864 Рік тому +7

    What kind of pen are you using? I’ve been looking for a fine-point pen for ages!

    • @EricBarger
      @EricBarger Рік тому

      I'm glad someone else asked this question.

  • @MotivationEditzG
    @MotivationEditzG 10 місяців тому

    Can somebody help me with this question:
    task:
    Arthur and Renate are playing on a square game board divided into 7 x 7 squares. Arthur has two red stones initially placed in the bottom left and top right corner squares, while Renate has two black stones initially placed in the top left and bottom right corner squares. On their turn, a player selects one of their two stones and moves it to a horizontally or vertically adjacent free square. Arthur and Renate take turns, with Arthur starting. Arthur wins if, after a finite number of moves, his two stones are in horizontally or vertically adjacent squares. Can Renate prevent this by making clever moves?

  • @itsalecsteica5243
    @itsalecsteica5243 Рік тому +11

    If this is a math-olympiad question, I'm a genius

    • @eliasbram3710
      @eliasbram3710 Рік тому +2

      do you all Know that math olympics have some simple questions here and there to slow participants down and reward faster solutions right?
      This Its ONE example of such questions. You solve it quickly to have more time to solve the actual problems
      Good luck with the other questions "genius"

    • @kjetilho
      @kjetilho Рік тому +3

      This shows a technique, it is kept simple to make the point come across more easily. In a real question, this could be one step in the middle.

    • @novaastronomia8720
      @novaastronomia8720 11 місяців тому

      you're right: its not a math olympiad question. Clickbait

    • @Ispeakwithlogic
      @Ispeakwithlogic 8 місяців тому

      It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡

    • @vot5748
      @vot5748 Місяць тому

      ⁠@@eliasbram3710math olympiad problems usually have a trick to them that isn’t commonly known, that’s why they are so hard. this however, is a textbook example of denesting square roots most people interested enough in contest math algebra would know. unfortunately, it is clickbait. this is not a MO level problem

  • @rajatshubhrosengupta284
    @rajatshubhrosengupta284 3 місяці тому

    Simpler n Shorter Solution :
    3 - 2 x Sq Rt of 2 = Z x Z
    OR
    Square of Z =
    3 - ( 2 x 1.41 )
    = 3 - 2.82
    Therefore
    Sqr of Z = 0. 18
    So Z = Sq Rt of 0. 18
    Answer = 0. 424

  • @Ramkabharosa
    @Ramkabharosa Рік тому +12

    √{a ± b√c} (a,b,c non-neg. rat.) can be simplified to √y±√z iff {a² - b².c} = d².
    If this d exists, then take y = (a+d)/2 & z = (a-d)/2. Here a=3, b=2, & c=2.
    So d = √{3² - 2².2} = √{9 - 8} = √1 = 1. So y = {3+1}/2 = 2 & z = {3-1}/2 = 1.
    Hence √{√9 - √8} = √{3 - 2√2} = √y - √z = √2 - √1 = (√2) - 1.

  • @Omar041
    @Omar041 8 місяців тому

    3-2root2=(root2-1) square under root square and roof goes the answer is root2-1

  • @stevethackery9853
    @stevethackery9853 Рік тому +80

    Sadly I was totally confused. She showed us a rather lengthy process, but with ABSOLUTELY NO explanation for why we are doing all these arcane steps. I think this is probably the worst possible explanation of how to achieve the objective, because she showed us WHAT to do but with no explanation at all of WHY.

    • @forvm2051
      @forvm2051 Рік тому +10

      Actually a lot of Math teachers I met explain things in this way, which can be rather frustrating

    • @albertoflanolombardo4155
      @albertoflanolombardo4155 Рік тому

      What do you expect from an Asian?

    • @somgesomgedus9313
      @somgesomgedus9313 Рік тому +8

      I would say that's not her fault but more the fault of mathematics. There is no rule or formula to ever tell you what to do next. In mathematics the only good answer to why did you do this is "because it works"

    • @Sevan59
      @Sevan59 Рік тому +4

      Sometimes I ask my self what is the benefit of such math, it is like guessing not a direct math , useless in normal job life , don’t expect nowadays mobile / comp. generation children need such bla bla

    • @stevethackery9853
      @stevethackery9853 Рік тому +16

      @@somgesomgedus9313 Actually I must respectfully disagree. To suggest that "because it works" is the only explanation needed in maths encourages rote learning, instead of gaining a true understanding of what you are doing, and why. Mathematics is a language used for the manipulation of symbols: "because it works" is like learning the words of a spoken language without learning their meaning. It renders you helpless when faced with a novel situation, and that is not how we should teach maths.

  • @ommapodi
    @ommapodi 9 місяців тому

    Don't make it complicated
    Sqrt(√9-√8) = sqrt(3-2√2)
    (If you think about it 3=1²+√2² also 2√2 is 2*1*√2 so it matches with (a+b)² = a²+b²+2ab )
    So,
    Sqrt(3-2√2) = sqrt(1²+2√2²-2√2)
    =Sqrt((1-√2)²)
    =1-√2
    Of it can also be √2-1 because of sqrts

  • @brettmoore3194
    @brettmoore3194 Рік тому +9

    Funny i always thought algebra was magical until i learned trigonometry. Then i was amazed on how it is used in daily life. I always questioned when i would need to use algebra in daily tasks... 😅

  • @AdityaKumar-gv4dj
    @AdityaKumar-gv4dj 10 місяців тому +1

    Root 2 - 1, solved in less than a second orally 😅, a better version of the problem always appears in school level maths olympiad so just used to it.

  • @tenantjames2967
    @tenantjames2967 11 місяців тому +3

    I love maths but the way she explains it its juicy way of explaining.

  • @kumardigvijaymishra5945
    @kumardigvijaymishra5945 5 місяців тому

    Trick is in figuring out the algebraic identity applicable to the Olympiad question

  • @luanpassoni
    @luanpassoni 9 місяців тому +2

    I never used the (a±b)² formula like that before, thats brilliant

  • @ricofarrari1346
    @ricofarrari1346 11 місяців тому +7

    Your just doing the math there’s no explaination along the way.

  • @KSJGaming
    @KSJGaming Рік тому +1

    Shortcut √3-2x1.4=0.447, just compare from the options

  • @MUTAA_MESTRI
    @MUTAA_MESTRI Рік тому +13

    Im very weak in math but somehow completed intermediate with 97% in math and completed my engineering a month ago 😂

  • @lilserotoninboost
    @lilserotoninboost 6 місяців тому +2

    Please give any practical use of learning this?

  • @rainbownneon900
    @rainbownneon900 Рік тому +28

    As an Indian, I appeared this question at SOF Mathematics Olympaid in my third grade

    • @JamesAnderson-lq8tf
      @JamesAnderson-lq8tf Рік тому +1

      I always see Indians in comment section only to brag about themselves. Usually this means a lack of confidence and self-respect. Is India one of the leaders in technology in the world?

  • @ellentau427
    @ellentau427 Місяць тому +1

    By the time she finished the square root I was SQUARE DANCING 😁

  • @polluxsimracing3712
    @polluxsimracing3712 Рік тому +5

    I got the answer as soon as i saw it 😂 i remember 40 years ago my teacher still be asking for the pointless work lol

  • @dillipkumardash433
    @dillipkumardash433 2 місяці тому +1

    We have Ramanujan Technique to solve this in the mind itself.

  • @leventaa2347
    @leventaa2347 Рік тому +64

    As a Turkish student who studied for university entrance exam, I am really sad that I solved this question like in seconds from my mind.

    • @egeozel80
      @egeozel80 Рік тому +6

      So which University did you end up 😬 😁

    • @vornamenachname906
      @vornamenachname906 Рік тому +6

      ​@@SunriseLAWroasted

    • @reinach77
      @reinach77 Рік тому

      Funny how so many third world students come here to brag about being able to solve this.

    • @jonavuka
      @jonavuka Рік тому +2

      ​@@egeozel80hes cleaning washrooms for a living

    • @omerece5011
      @omerece5011 11 місяців тому

      In1990ies in ist. muhendislik one of our friend proved a wellkown physics equation's incorrectnessby maths but these kids are smiling on you ,dont worry you're in the right path...

  • @ruqeyyarsulova4032
    @ruqeyyarsulova4032 8 місяців тому

    I am an Azerbaijan pupil. Question is very easy. I found the solution to the question as soon as I saw it

  • @Lincoln-ht2dv
    @Lincoln-ht2dv Рік тому +3

    I don't like abstract short cuts. Too complicated.

  • @_dr.mayhem
    @_dr.mayhem 2 місяці тому +1

    I am a student
    Can you tell me what I did wrong trying to solve this
    √((√9)-(√8))= x
    √9-√8=x²
    9-2×√9×√8+8=x⁴
    9-2×3×2√2+8=x⁴
    17-12√2=x⁴
    x=fourth root of 17-12√2
    But the answer I'm getting is 0.4142135.....
    Which is also the same answer I'm getting for √(√9-√8). (0.4142135.....)
    Edit: I'm an idiot I thought you said the answer is sqrt of 2, didn't hear the part where you said sqrt of 2 -1, that makes a lot more sense. So my answer is correct.

  • @msanio1
    @msanio1 Рік тому +6

    Please do not write sqrt(2)= 1,414 This was the moment when you lost me.

    • @NickLea
      @NickLea Рік тому +1

      @@buddy0479 You are mistaken. In the UK it is also 1.414. It is other European countries such as France and Germany where this occurs.

  • @alwoolridge6377
    @alwoolridge6377 Рік тому

    I like maths...but I absolutely hate when they get "creative" (i.e.: the only way to resolve a problem, instead of using a well stablished and proven algorithm, is having a happy idea). Thank God for calculus.

  • @sureshmukhi2316
    @sureshmukhi2316 Рік тому +18

    Why does the final answer have to be positive?

    • @flam1ex186
      @flam1ex186 Рік тому +6

      the root of x square = module x(module≥0)

    • @sureshmukhi2316
      @sureshmukhi2316 Рік тому +1

      @@flam1ex186 a square root can be both positive and negative

    • @evgtro8727
      @evgtro8727 Рік тому +15

      @@sureshmukhi2316 that is true for complex numbers/functions. For reals it must be positive.

    • @kasiviswanath2623gzujejs
      @kasiviswanath2623gzujejs Рік тому

      Root doesn't contain negative

    • @sureshmukhi2316
      @sureshmukhi2316 Рік тому

      If a root can't be negative then explain the quadratic formula?

  • @glasssmirror2314
    @glasssmirror2314 9 місяців тому

    My friends please don't crack your heads. Here the teacher should have said that this works as Quad Eq with 3 and a number inside radical i.e 2 so 2+1=3 and 2x1=2 so a=2 and b=1

  • @satwikshaw1031
    @satwikshaw1031 Рік тому +3

    As Indian I can confirm this we did in grade 6

  • @anhnl1992
    @anhnl1992 Рік тому

    Replace by =

  • @WoodrowWoods2007
    @WoodrowWoods2007 Рік тому +21

    It would be interesting to see this used in an actually useful use case. My brain has a hard time following nonsensical “just because” problems

    • @lestath2345
      @lestath2345 Рік тому +3

      What do you define as an actual "useful use case"?

    • @somgesomgedus9313
      @somgesomgedus9313 Рік тому

      Find the roots of x^4-6x^2+1

    • @WoodrowWoods2007
      @WoodrowWoods2007 Рік тому +5

      @@lestath2345 tell me a real world instance where this would be used other than a math class

    • @lestath2345
      @lestath2345 Рік тому +8

      @@WoodrowWoods2007 In the field of pure math. Also, we're mostly doing this for the sake of doing it, just like playing video games, *for fun*.

    • @Aman-nk5uq
      @Aman-nk5uq Рік тому

      ​@@lestath2345yes it is a brain exercise. Opens the horizons of brain

  • @Eismann1
    @Eismann1 Рік тому

    It's a nice problem and thanks for your video. Please however do not write "=>" when dealing with terms. It leads many students to improper notation.

  • @victory2115
    @victory2115 Рік тому +3

    Why ? 😳🤷‍♂️

  • @BrunoPessolani
    @BrunoPessolani Рік тому +1

    The answer is [2(square root) - 1]

  • @anatolykarpov1821
    @anatolykarpov1821 Рік тому +6

    In Asia, a bad student in 2nd school can easily do this math :))

  • @IsaacAsimov1992
    @IsaacAsimov1992 Рік тому +1

    Oh, that voice, that accent! ❤️

  • @dis5422
    @dis5422 Рік тому +4

    Очень легкая и известная задача

    • @PankajKumarRoy-q2z
      @PankajKumarRoy-q2z Рік тому

      Средний вопрос олимпиады по математике в Юпитере

    • @oqui7009
      @oqui7009 Рік тому +3

      Ключевое слово "известная". Всё легко и просто, когда известно. Жаль, что до людей не доходит элементарная вещь

  • @AbsarHussain-ou5bv
    @AbsarHussain-ou5bv 5 місяців тому

    I can do it shortly as to remove the whole square root and give power on both and cancel the square in to second rood know we get 9-8 and ans would be 1

  • @cspresimir
    @cspresimir Рік тому +6

    Kinda useless for ANY practical purposes ...sqrt(sqrt(9) -sqrt(8)) is solved using a pocket calculator

  • @rameshguru5659
    @rameshguru5659 Місяць тому

    I was able to answer in first glance it it has roughly taken me a 30-35 seconds..
    If you have already practised this type of questions then this wont really take time you can by a shortcut also that you should know if you are in 9th or above

  • @Pietras_Maestro
    @Pietras_Maestro Рік тому +9

    Very interesting, although in practice it is not needed for anything in life :)

    • @chrisjfox8715
      @chrisjfox8715 Рік тому +9

      In everyday life no, but the general take away from problems like this is exercising the notion of manipulating mathematical expressions into different forms to make them simpler (i.e., easier to manage, interpret, etc).
      This particular example isn't that complicated, but the general skill of simplification can come in handy in certain jobs. Like if one were to come up with a certain formula to describe a particular phenomena that's unique to that company, someone else may want to manipulate the form of that formula so to make its terms more explicit.

    • @anuragparasharsarmah1045
      @anuragparasharsarmah1045 Рік тому

      ​@@chrisjfox8715bruh

    • @PlatuzCubing
      @PlatuzCubing Рік тому +2

      Certainly you won’t need it don’t worry

    • @An_ony_mous
      @An_ony_mous Рік тому

      It's just for improving your thinking skills.

    • @CIAinTaiwanAndUkraine
      @CIAinTaiwanAndUkraine Рік тому +3

      You don't, but the smart people do

  • @nomobo1778
    @nomobo1778 2 місяці тому

    Solved it in my head in less than 3 seconds, and I am 81. Of course I learned math before they “improved it.” And the instructor is wrong. The answer is 1.

  • @priyanshisharma2750
    @priyanshisharma2750 Рік тому +3

    This is actually really simple for an olympiad 😂

    • @sritam_mirdha
      @sritam_mirdha Рік тому

      I have a backlog in math, so not a qualified person to address this, but any question is hard if you don't know the method to solve it. You know this already, sweetheart...❤

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  • @ImDaNoobbruh
    @ImDaNoobbruh 6 місяців тому

    This will not come in SG math olympiad. they be testing quadratic formula and equations for junior.

  • @Benjybass
    @Benjybass Рік тому +3

    I fell asleep at 0:23.🥴

  • @pandurangaraonimmagadda9966
    @pandurangaraonimmagadda9966 Рік тому +1

    Answer : root of(3-2root2)=root 2-1

  • @caydeniam123
    @caydeniam123 2 місяці тому

    Im in 9th grade and know how to do this. So ez.
    sqrt of 9 = 2 x sqrt 2.25
    sqrt 8 = 2x sqrt 2
    2xsqrt2.25 - 2xsqrt2= 2xsqrt 0.25=2x0.5=1

  • @superman00001
    @superman00001 Рік тому +2

    You’re clever and gorgeous ❤❤❤

  • @Spaced_Invader
    @Spaced_Invader 8 місяців тому

    I suck at maths, but found this very calming. Please advise using the problem above, where would I use it in life? Many thanks....

  • @Tommy-C-Nguyen
    @Tommy-C-Nguyen Рік тому +2

    sqr(9) = +/- 3 NOT 3. The same for sqr(8) is +/- 2.sqr(2). You only solve a half of the problem.

    • @oZqdiac
      @oZqdiac 9 місяців тому +1

      Sqrt(9) is always 3 because there is something called the principal square root and it can only yield positive answers
      For example
      x = sqrt(9), x = 3 because of the principal square root
      However if the equation was x^2 = 9, that’s when x can be +/- 3.

  • @thevijaykumar
    @thevijaykumar 4 місяці тому

    It's been 4 years since I graduated from college and I'm having a job and I could still solve it without using paper and pen.

  • @tinathorson4578
    @tinathorson4578 10 місяців тому

    So why isn’t the answer .414? Why stop 1 step short like that?

  • @enes3573
    @enes3573 Рік тому +1

    Bu soruları Türkiye'de ilkokul çocuğu çözüyor.
    Primary school children solve these questions in Turkey.

  • @samisam7190
    @samisam7190 Рік тому +1

    A lot of work while there is simpler shot cut . Where did a and b come from

  • @pavlecvoric5200
    @pavlecvoric5200 Рік тому +2

    37 years ago I had this one i my final high schools exam

  • @madmaxx5280
    @madmaxx5280 Рік тому +1

    Even though she is flexing she got the answer wrong it should be 0 .414