Math was always my favourite subject in school but ever since college I lost touch with it. Seeing your videos makes me want to solve algebra, differential and calculus again 😄
thinking about it geometrically makes it easier. solving two equations meant to find the points where the st line interests/touches(if only had 1 solution) the circle. and then add the coordinates for required answer
Nostalgia!!! For a minute, I thought I was once In my high school. What a days it was! My professor was teaching us on white board and we compete with each other for getting answer first!! ❤
For some reason Andy's vids got suggested to me a couple weeks ago. They are satisfying for some reason. I think it's the presentation. Bonus on this one: I appreciate the plot at the end here. Anyway, thanks.
I solved this in my head by imagining a circle of radius 5 located at the origin and a linear equation with intercept of 10 and slope pf negative 2. I then just guessed and checked integer values to see where they would intersect. I suppose this doesn't work for more complicated examples, but it worked nicely here!
Try This🙃 - Q. The smallest value of k, for which both the roots of the equation, x^2 - 8kx + 16(k^2 -k +1) = 0 are real, distinct and have values at least 4, is [JEE 2009] Ans. 2
I like just thinking of the formula as "first term squared + second term squared - twice the product". Makes a psychological difference for me at least. It doesn't require me first setting up (a+b)^2 as (a+b)(a+b).
Solved this in less than a minute without even needing the second equation. Just looking at x^2+y^2=25 immediately made me think of the classic 3, 4, 5 right triangle, where 3^2+4^2=5^2, with 5^2 being 25. This tells me that x and y are 3 and 4, doesn't matter which, as the question just asks what x+y equals. 3+4=7, and that's the answer. The second equation really just determines what x and y specifically are, as 2*3=6, and 6+4=10, therefore x=3 and y=4, though you don't need to know which is which specifically for this problem.
@@jonstiffer4994 actually his method kinda works, you convert the first equation into a² + b² = c² and then you can see the 3,4 solution, but you can also deduce that 0,5 is a solution. So it kinda works :-)
There could be possibly multiple solutions on this one, and thanks to the guy for breaking it down for us. You only found 1 solution, though it works since you found a solution after all.
It's always "or" because you always assume that one of the factors equals zero, not both of them. It is either one or the other, but not both at the same time.
@@JGSstudios in this example if x equals 3, you plug it in and find that it simplifies to 0 * 2, so the second term is not 0. Thats why its or and not and
Якщо графічно, то перше рівняння - це коло з центром у точці О(0;0) і радіусом в 5 одиничних відрізків, друге представляємо, як у=-2х+10, це лінійна функція, для її побудови достатньо рівно з'єднати дві точки, які її задовольняють, два числа підставляємо по черзі замість х і через нього виражаємо у, третя - теж лінійна, так само як і з другою, але там вже у=-х, далі теж знаю що робити, і як способом підстановки можливо, але лінь писати.
When you say, in the min 1:42, that it can be "x-3=0" or "x-5=0". Why don't you think that both can be zero and that way you can say that x=0? I mean 0 multiplied 0 it is 0... After that you can see that this cannot be the answer because y would not be the same number in both equation, but it's just an doubt. (Sorry for my English, not my first language) I say this because my teachers always forced us to think about the X being 0!
When you went from x^2-8x+15=0 to (x-3)(x-5)=0, I was like "What do you mean, factorize? How?" because I was only ever taught this weird thing where you go x = -(p/2) +/- squareroot of ((p/2)^2-q), and you find p and q via this 0=x^2+px+q Is this just taught differently in different countries? Because your way seems so much easier and now I'm just angry at my math teacher...
Thumbnail doesn't say what the restrictions are. The pairs I get for (x, y) are (5, 0) and (3, 4). So if x and y must be positive, the ? is 7. Otherwise, it could also be 5, because if we solve for ? we get a quadratic that simplifies to ? = 6 +/- 1.
Dang it, I forgot to square the y figure once I had -2x+10. Somehow I came out with one of the answers being the same. I hade to quadratic formula it, but I got x being 5 or -3 and y being 0 or 4 respectively. But I see where my mistake was. Dang.
You could skip the step or calculating y. Once you have calculated x you know from the second equation that the value you want is 10-x. If the end result is a function of multiple variables you often don't actually need to calculate all the variables to get the answer.
This was unnecessary Andy. X^2 + Y^2 = 25 is the formula for a circle radius 5 around the origin. Once you are dealing with a circle radius 5 your antennae should be suspicious of a 3-4-5 triangle, and lo and behold: Twice 3 Plus 4 Equals 10! Algebrae not required!
Wouldn't you just get the square root of X and Y in the first one, seeing that X+Y is 5? That's what the problem is asking, what is X+Y. We don't really need to know what they are to know the answer to that.
Massive overcomplication, using a very basic simultaneous equation you 4x^2 +y^2 = 100 and x^2 + y^2 = 25 simplifying to 3x^2 = 75 thus x = 5 and y = 10-2*5 = 0, thus x= 5 and y= 0
how? you cannot root x^2 + y^2 like that ... if you root x^2+y^2 ... the square root will be x^2 + y^2 + 2xy - 2xy = 25 => (x+y)^2 - 2xy = 25 => root of [ (x+y)^2 - 2xy ] = root of 25 => x+ y - root of 2xy = 5 and yeah you have to realise that x^2 + y^2 is not the same as (x+y)^2....Its fine we all make mistakes but with that equation that was a big blunder
You my young friend have a beautiful mind, you leave me speechless, do you have a channel that can help young American children. Your brain is most definitely not in question. But..putting that into layman's terms to help struggling children would be a God send to the. Have you ever seen the movie where Ryan Reynolds plays a teacher...wow if I had him in school, learning would have been an adventure, could you take that challenge 😃😉💞💞💞💞👋😃🦘🇦🇺🐨💫.
Math was always my favourite subject in school but ever since college I lost touch with it. Seeing your videos makes me want to solve algebra, differential and calculus again 😄
3^2 + 4^2 = 5^2 being my favourite pythagorean triplet makes this so easy for me.
The 3, 4, 5 right angle triangle is the classic example.
@@ChaosPodanytime I see the sums of two squares to be 25 I immediately go to 3,4,5.
It made it harder for me because it caused me to overlook 5 as a solution
@@dimitardonev4507Это работает только в том случае, если x и y - целые числа.
thinking about it geometrically makes it easier. solving two equations meant to find the points where the st line interests/touches(if only had 1 solution) the circle. and then add the coordinates for required answer
Nostalgia!!! For a minute, I thought I was once In my high school. What a days it was! My professor was teaching us on white board and we compete with each other for getting answer first!! ❤
The way you breakdown the math problems makes me revisit my old high school math and solve problems! You’re doing a great job!
I'm here completely by accident. And I'm terrible at math... This is going to change.
How are you now?
X=3 and Y=4 satisfies the original equations.
Brain fart X=5 and Y=0 works too.
Both
X + Y = 3 + 4 = 7
X + Y = 5 + 0 = 5
x,y>0
For some reason Andy's vids got suggested to me a couple weeks ago.
They are satisfying for some reason. I think it's the presentation.
Bonus on this one: I appreciate the plot at the end here.
Anyway, thanks.
I solved this in my head by imagining a circle of radius 5 located at the origin and a linear equation with intercept of 10 and slope pf negative 2. I then just guessed and checked integer values to see where they would intersect. I suppose this doesn't work for more complicated examples, but it worked nicely here!
Andy math : How exciting
Me : please keep math as far as possible from me
Try This🙃 -
Q. The smallest value of k, for which both the roots of the equation,
x^2 - 8kx + 16(k^2 -k +1) = 0 are real, distinct and have values at least 4, is [JEE 2009]
Ans. 2
how is this done? sorry im only in 10th class
@@droftrop4135That question is from Quadratic equation chapter . I'm in class 10 too
The answer is 1
I immediately saw the Pythagorean triplet. 3/4/5
I like just thinking of the formula as "first term squared + second term squared - twice the product". Makes a psychological difference for me at least. It doesn't require me first setting up (a+b)^2 as (a+b)(a+b).
I bare an extreme hatred for math, then explain to me how the heck did this feel like a fun little puzzle.
Well very nice 🙂
I like it ♥️
We can easily see the triplet 3²+ 4² =5² and we get 3 and 4 for x and y
Done lol
You'd be half right because that's only one of the answers
It must the math teacher's method, or you get no points/marks for whatever shit you've done in your brain!😂
I looked at x^2-8x+15=0 and went to bhaskara that out of nostalgia 😅
Immediately knew it was 3 and 4. Know your pythagorean triplets!
Solved this in less than a minute without even needing the second equation. Just looking at x^2+y^2=25 immediately made me think of the classic 3, 4, 5 right triangle, where 3^2+4^2=5^2, with 5^2 being 25. This tells me that x and y are 3 and 4, doesn't matter which, as the question just asks what x+y equals. 3+4=7, and that's the answer. The second equation really just determines what x and y specifically are, as 2*3=6, and 6+4=10, therefore x=3 and y=4, though you don't need to know which is which specifically for this problem.
You still need to go through the steps incase there are other solutions, like in this case
@@martonbalazskajari5424 I don't think he wathed until the end. He wass too busy bragging in the comments. :)
@@jonstiffer4994 actually his method kinda works, you convert the first equation into a² + b² = c² and then you can see the 3,4 solution, but you can also deduce that 0,5 is a solution. So it kinda works :-)
you only found one of the solutions
There could be possibly multiple solutions on this one, and thanks to the guy for breaking it down for us. You only found 1 solution, though it works since you found a solution after all.
use Pythagorean triplets, 3,4 and 5.
I saw thumbnail and immediately remeber Pythagoras triplet...and it satisfied the second question....7 EASYYY
dumb question, but why is it "or" and not "and"?
I might be wrong, but I think it's because X and Y can only be one number in this ex. , so its one *or* the other
@@Logia_ but it’s always or
It's always "or" because you always assume that one of the factors equals zero, not both of them. It is either one or the other, but not both at the same time.
@@JGSstudios in this example if x equals 3, you plug it in and find that it simplifies to 0 * 2, so the second term is not 0. Thats why its or and not and
x+y cant be 7 and 5 because 7 doesn't equal 5
Якщо графічно, то перше рівняння - це коло з центром у точці О(0;0) і радіусом в 5 одиничних відрізків, друге представляємо, як у=-2х+10, це лінійна функція, для її побудови достатньо рівно з'єднати дві точки, які її задовольняють, два числа підставляємо по черзі замість х і через нього виражаємо у, третя - теж лінійна, так само як і з другою, але там вже у=-х, далі теж знаю що робити, і як способом підстановки можливо, але лінь писати.
I have no idea how but in under 30 seconds I got it right, without any of the equations he did
When you say, in the min 1:42, that it can be "x-3=0" or "x-5=0". Why don't you think that both can be zero and that way you can say that x=0? I mean 0 multiplied 0 it is 0...
After that you can see that this cannot be the answer because y would not be the same number in both equation, but it's just an doubt. (Sorry for my English, not my first language)
I say this because my teachers always forced us to think about the X being 0!
y . z = 0, so y = 0 and/or z = 0. procedure is the same. instead i like using the quadratic formula
When you went from x^2-8x+15=0 to (x-3)(x-5)=0, I was like "What do you mean, factorize? How?" because I was only ever taught this weird thing where you go x = -(p/2) +/- squareroot of ((p/2)^2-q), and you find p and q via this 0=x^2+px+q
Is this just taught differently in different countries? Because your way seems so much easier and now I'm just angry at my math teacher...
Thumbnail doesn't say what the restrictions are. The pairs I get for (x, y) are (5, 0) and (3, 4). So if x and y must be positive, the ? is 7. Otherwise, it could also be 5, because if we solve for ? we get a quadratic that simplifies to ? = 6 +/- 1.
I saw x^2 + y^2 = 25 and I went strait to 3,4,5 triangle. Then I thought 3+3+4 = 10 which also works so then I did 3+4 = 7.
I'm not really good at math, but I got the right answer just by thinking: which two numbers, when squared, sum up to 25?
Dang it, I forgot to square the y figure once I had -2x+10.
Somehow I came out with one of the answers being the same. I hade to quadratic formula it, but I got x being 5 or -3 and y being 0 or 4 respectively.
But I see where my mistake was. Dang.
Well there was a part in this video where you could’ve use 2nd grade ecuation and it would’ve made it much easier
I think I remember doing this exact problem before and I hate it
x = 5, y = 0
got the answer by guessing that x was 3 and y was 4
7 ...took 2 secs
Still only half correct 🤡
Or 5
I did this mentally idk how but I did
X^2+y^2=25
(X+y)^2=25
X+y=5
Im an 8th grade student and i solved it in 30 seconds
Eu bati o olho e já sabia qual era kkkk
Hello everybody, today we gonna do 3 grade's excersises.
Kindergartenses, pants with harnesses
too easy that i solved it through thumbnail
people mention why I don't do this shortcut...
Well I did 😝 😝 😝 😝 😝 😝
X=5 Y=0 also works
i made a dumb guess, that if I square root x² and y² that will be 5 hahaha and it turns half out right...
Got 5,0🎉🎉🎉
I just square rooted everything in the first equation
Not correct process.
Ik
x = 3 and y = 4
0and 5
What is fun here? The most common task for 6 class in Russia...
I think you mean MATHS, how many more times have I got to say, Mathematics is plural not singular so you can't have a MATH.
0:32 Bro why you (a-b)(a-b)? Can you just (a-b) ² = a²-2ab+b²?
Prediction: x=5, y=0
X=3..y=4
I took the square roots of both the sides and find x+y
:- √x^2 + √y^2 = √25
= x + y = 5
So is it correct?
Theres two answers, you got one of them correct
7 and 5 will be Correct answer
Super easy for grade school
Would somebody be kind enough to explain why we are allowed to divide by 0 at 1:18?
We’re not dividing by 0 we’re dividing by 5
Oh, I missed (5,0) solution.
2x + y = 10
So, x+y = 10/2 = 5
X+y = 5
Simple as that 😂
Exactly, someone explain why he went through all of that to get x+y= 7 or 5
How Excting! 🙂
this question is secondary school level in Türkiye
You could skip the step or calculating y. Once you have calculated x you know from the second equation that the value you want is 10-x. If the end result is a function of multiple variables you often don't actually need to calculate all the variables to get the answer.
5?
x = 5 y = 0?
7
16
X is 5 and Y is 0
Didn't watch the video because I'm at work rn,,is the answer x=3 and y=4?
That's half the answer
why don't you just sqare root the first one and you get your answer?
√{a²-b²} is not the same as (a-b)²
@@Alolan533 ooooh actually yeah that makes sense 😅😅😅😅
Was it that we couldn't square root both sides straight away in the dirst equation?
This was unnecessary Andy.
X^2 + Y^2 = 25 is the formula for a circle radius 5 around the origin. Once you are dealing with a circle radius 5 your antennae should be suspicious of a 3-4-5 triangle, and lo and behold: Twice 3 Plus 4 Equals 10!
Algebrae not required!
Result is 7
X+Y=7 ou X+Y=5
Wouldn't you just get the square root of X and Y in the first one, seeing that X+Y is 5? That's what the problem is asking, what is X+Y. We don't really need to know what they are to know the answer to that.
x is 3 and y is 4, which add up to 7.
@@spagootest2185 *Or* X is 5 and Y is 0, which add up to 5.
@@ShursGarden true!
Sqrt(x^2 + y^2) is not equal to x + y. In fact x+y squared is x^2 + 2xy + y^2......
Simple. Just take the first equation, and sqrt both sides. Since (x+y)^2=x^2+y^2, we get x+y=5.
Nhìn là biết 3,4
What about x=5 y=0
Whoops I typed this looking only at the comments didn't watch the video first lol
Bruhh... In India we used to solve these type of problems when we were in 8th class...
You should Try To solve the problems of JEE adv. 😶🌫😶🌫
Stop being a smartass ehn!
Bro, if x^2 + y^2 = 25, then x+y = the square root of 25 which is 5. Bro just complexified this equation for no reason 😂
Massive overcomplication, using a very basic simultaneous equation you 4x^2 +y^2 = 100 and x^2 + y^2 = 25 simplifying to 3x^2 = 75 thus x = 5 and y = 10-2*5 = 0, thus x= 5 and y= 0
You missed a solution then
If u want to multiply one side by 4 u need to do so on the other side too leaving u with 4(x^2+y^2)=100, which then equals 4x^2+4y^2=100
@JD-ee4df nah he was just lucky he even git one of the solutions
a standard turkish student laughed this question
DİMİ SOK GECİRDİM TEKLİ SORU ÇÖZÜMÜ ARARKEN KARŞIMA BU ÇIKINCA
√x^2 + √y^2 = √25
x+y=5
No, u need to √ both sides leaving u with √x^2+y^2=√25. U cant shortcut when its addition, only when its multiplication.
why dont u just use a square root in every term of the equation and get 5 instantly
That's not how it works
This is so over complicated jus do the cancel method
It isn't
Actually no not "how exciting"! How is this not elementary school math?
The working is high school level. You cant just say that the triplet 3^2 + 4^2 =5^2 and give that as your answer
Most easiest answer 👇
x^2+y^2 = 25
Give root both side
x+y = 5
how? you cannot root x^2 + y^2 like that ...
if you root x^2+y^2 ... the square root will be
x^2 + y^2 + 2xy - 2xy = 25
=> (x+y)^2 - 2xy = 25
=> root of [ (x+y)^2 - 2xy ] = root of 25
=> x+ y - root of 2xy = 5
and yeah you have to realise that x^2 + y^2 is not the same as (x+y)^2....Its fine we all make mistakes but with that equation that was a big blunder
Half answer with absolutely wrong calculation
You my young friend have a beautiful mind, you leave me speechless, do you have a channel that can help young American children. Your brain is most definitely not in question. But..putting that into layman's terms to help struggling children would be a God send to the. Have you ever seen the movie where Ryan Reynolds plays a teacher...wow if I had him in school, learning would have been an adventure, could you take that challenge 😃😉💞💞💞💞👋😃🦘🇦🇺🐨💫.
7 işte amuğa goyim
Im an 8th grade student and i solved it in 30 seconds
x = 5, y = 0
7
7
And 5
7
And 5
7
And 5