Luxembourg - Math Olympiad Question | You should know this trick
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- Опубліковано 12 чер 2023
- 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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I am a genuine maths dunce. Don't remember learning any of this and I don't understand it now either! 😅
Every one has their own unique talent sir....
Bro are you from America 😂
@@user-qs7pr7kl2jif you think Americans are dumb you should see which country has the most medals in International Math Olympiad
It is too simple for Math-Olympiad.
Agreed
No
@@furina9053Olympiad math is just a whole different level man, thats why they mentioned it
I think it was maybe paralympic games
Maybe it was from the qualifier level exam
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.
Bro this for real made me fall of my bed laughin
She got this "trick" out of a Deus Ex Machina
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.
Lies again? Must See TV Deaf Blind
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))
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.
So -1 is on of your answers for a square root problem? What times what equals negative 1?
Ooops...
As a martian, I teached myself this trick at 6 months old, by observing shadow patterns in our red planet.
😂
Ain't no martian looks like a mongoose 🗣️
One should be careful in distinguishing between 'equals' and 'implies' symbols.
We were solving such problems in my 8th grade in Romania in a regular maths class. Too simple for an Olympiad.
no one cares
I'm sure third world Romania isn't.
I wonder if no baddy needs mathema😊ticks why still teach them
Cope and seethe.
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.
√(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.
i didn't get your point
@@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.
@@jim2376made even more difficult 😂 , what is a radicand ? Too simple earlier , it happens by simple instincts
@@abhishekchhikara4100That's for people like you, just go and read definitions and you can see the word radicand is so common in most textbooks
What happens when your teacher wants to see the problem worked step by step?
I could have gone my whole life without knowing that answer! Now I know!
Please help me to solve using diff of 2 sq as mentioned by teacher but not followed.
Interesante y didáctica explicación, muchas gracias por compartir 😊❤😊
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.
Then again, the square root of 9 is also -3, so there are two answers.
@@scottrichmond3548 square root of 9 is 3 not -3
@@rudraroopbhattacharjee6191 what's -3 * -3 ?
@@antronx7 9
@@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
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.
yeah, it's an easy question. Like JEE Mains level probably.
@@eddie31415 this is class 9 school level.
This question is in Class 9 R D Sharma Factorisation of Polynomials fill in the blanks in the form of √3 -2√2.
@@eddie31415 lol no 8th or 9th class problem maybe jee mains level are far more harder than thiss
@@eddie31415 it's a grade 9th or 10th question maybe
Nicely done and thank you.
However, I'll just use my handy electronic calculator for these kind of problems.
I hope one day everyone finds the peace in math! Love from Türkiye.
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
it's for secondary school in Vietnam 😂
True story 😂
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
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.
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.
I am totally lost from the start.
I knew this ...i just forget about it. That's what happens when you don't stay in practice
Ashole cleaning in Hospital useless.
I never used the (a±b)² formula like that before, thats brilliant
This can’t be olympiad question. It is literally one of the math 101 rules. There is even shortcut for that like people mentioned.
do you 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
@@eliasbram3710 heh
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
Yupp, one must have known the patterns before
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
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😂🤡
"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.
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 .
I just did it like √(3-2√2)
√(3-2(1.4)
√(3-2.8)
√0.2
√20×10^-2
Which gives somewhere between 4~4.9 not 5 since it needs root 25 and taking out the 10^-2 from root gives us
4.1×10^-1 which gives us 0.41
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.
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.
@@lesouni9342 you don't need a calculator for such easy things.you don't even need a pen& paper for sure.
I love maths but the way she explains it its juicy way of explaining.
Shortcut √3-2x1.4=0.447, just compare from the options
What kind of pen are you using? I’ve been looking for a fine-point pen for ages!
I'm glad someone else asked this question.
37 years ago I had this one i my final high schools exam
Since Sq root of 2 -1 is positive you don't have to use absolute value
Used calculator, got same result.💪
Work smarter not harder 💪
This is a standard problem. You reduce it to sqrt (sqrt (9)+sqrt(8))=sqrt (2+2\sqrt(2)+1)=sqrt(2)+1.
I suck at maths, but found this very calming. Please advise using the problem above, where would I use it in life? Many thanks....
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.
It can be the other method which is great but the standard one is more easy and convinnient
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.
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?
Para los que piden solución negativa, recuerden que:
x^2=4
no es lo mismo que
x=√4
....
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
pero cuadrados negatvos no existen
Oh, that voice, that accent! ❤️
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.
If this is a math-olympiad question, I'm a genius
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"
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.
you're right: its not a math olympiad question. Clickbait
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😂🤡
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.
Go for ✓2 - 1 as an answer
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?
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)
@@TheMeiravital😂
@@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.
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
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.
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
As an Indian, I appeared this question at SOF Mathematics Olympaid in my third grade
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?
Trick is in figuring out the algebraic identity applicable to the Olympiad question
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... 😅
Brilliant 👏
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?
The answer is [2(square root) - 1]
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.
So which University did you end up 😬 😁
@@SunriseLAWroasted
Funny how so many third world students come here to brag about being able to solve this.
@@egeozel80hes cleaning washrooms for a living
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...
Answer : root of(3-2root2)=root 2-1
Under the bracket or under the root ?
Nice but where we can implement this kind of maths problems ?
I am an Azerbaijan pupil. Question is very easy. I found the solution to the question as soon as I saw it
Even though she is flexing she got the answer wrong it should be 0 .414
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
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?
Motivation being it's an olympiad question and already has an answer sadly. Kids training for math contests like this are used to the form of the math question so they only have to pull one trick out of the bag. It's the kind of stuff you have to rote learning!
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...
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😂🤡
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.
Can you specify the implies symbol?
Have you forgeten the first root ?
Who ever this woman is, I’m in love. Thank you x
"Under root of" = "Root over"
In Vietnam, normal students can do this test when they are in 9th grade
Im very weak in math but somehow completed intermediate with 97% in math and completed my engineering a month ago 😂
No one asked
@@AdityaKumar-gv4dj No one answered you! Saala
A lot of work while there is simpler shot cut . Where did a and b come from
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
Replace by =
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.
√(√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)
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
great stuff
Please give any practical use of learning this?
3-2root2=(root2-1) square under root square and roof goes the answer is root2-1
Why module of the solution in the end? The solution is already a number and also a positive one.
Nice
Loved it !
Loved it
Is 2** 1/2 -1 a simpler form than 3 - 2*2**1/2? Not by much!
It can be root 2 -1 or 1-root 2
Bu soruları Türkiye'de ilkokul çocuğu çözüyor.
Primary school children solve these questions in Turkey.
Where can find topics like this are they in college
Is there other way to solve this problem?
Where from it came? Totally confused.
How is that applied?
excelente
Thanks for lesson, great work
I think you should study more about modulus
Answer:sqrt2-1
She's talking about factoring
Do you need pen and paper for this ??
This came in math Olympiad? Plz can you confirm the you confirm the year and country
This is something you can do without even pen paper I don't think any country would lower their standard this much
This will not come in SG math olympiad. they be testing quadratic formula and equations for junior.
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.
Actually a lot of Math teachers I met explain things in this way, which can be rather frustrating
What do you expect from an Asian?
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"
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
@@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.
Bhai as a 9thee Indian this is way too easy for olympiad
Excelent !!!
Good!
Calculator 🗿
I done this by using Calculus and my answer came approximately equal
Please do not write sqrt(2)= 1,414 This was the moment when you lost me.
@@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.
Why not subtract under root of 8 from under root of 9
In India we had to solved this kind of questions in class 7 or 8 I guess.
2^(1/2)-1