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1) subtract eqn for y^2 from eqn for x^2, you get (x+y)=16. 2) add the eqns, x^2 + y^2 you get 18x + 18y. 3) Add 1 to both sides: 18(x+y) + 1 = x^2 + y^2 + 1 18(16) + 1 = x^2 + y^2 + 1 289 = x^2 + y^2 + 1 take sqrt of both sides, sqrt(289) = 17.
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In given relations ,by equality for (x+y) we get x+y=16...........now , add this two equations then we also get x^2+y^2=18(x+y) then x^2+y^2+1=(18)(16)+1=289 √x^2+y^2+1=17
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I wasn't sure that a pair of numbers exist that have a sum of 16 and a sum of squares of 288 but from investigation it appears that one number is approx 16.945 and the other is approx -0.945.
I'll explain that one in some other video. That'll be completely different way. Thanks for asking Thanks Bilal for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards
Not sure if you got the answer yet but, if you look at the video again, we found out that x+y=16. Thus, y=10-x. Substitute this new y-value in the first equation: x^2 = 17x + (16-x). We will now get to solve a quadratic equation for x: x^2-16x-16=0.
You and Presh Talwalker presented this problem BUT both of you got it incorrect: It's not (17+1)(17-1) or vice versa, solve and change the -1 to a +1 on the left side, then take square root of both sides. You are supposed to: MULTIPLY the 16*18 or vice versa first, getting 288, then ADD 1 to BOTH sides, then take the square root of both sides(this is why it is called an equation, meaning both sides have to be balanced in the equation), then solve. This is a simple math problem. Skipping steps gets points deducted in high school. You don't get extra points for skipping steps.
I have a different approach... X²+y²=18(X+y) √(18(X+y)+1)=z Z²= 18(X+y)+1 Now Euclid division...a number when divided by 18 leaves r=1 and that number is also a perfect square so the least value of X+y =16 ... 18*16+1=z² Z=17
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Beautiful techniques, great insight.
Glad you enjoyed it!
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You make solving difficult problems so easy. Such a pleasure to watch your channel sir
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1) subtract eqn for y^2 from eqn for x^2, you get (x+y)=16.
2) add the eqns, x^2 + y^2 you get
18x + 18y.
3) Add 1 to both sides:
18(x+y) + 1 = x^2 + y^2 + 1
18(16) + 1 = x^2 + y^2 + 1
289 = x^2 + y^2 + 1
take sqrt of both sides, sqrt(289) = 17.
Beautiful and smart. This could make a math contest question for middle school students.
Bahut khub 🌹🌹🌹🇮🇳
beautiful...
Once you get to x2+y2= 18*16 the problem is over don’t need to worry about (17+1)x (17-1) can just multiply it add the 1 and take sqrt
Sir,
On the first look the problem seems to be a difficult one.
But when you work it out, it becomes so easy.
It is wonderful.
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Love and prayers from the USA!
Hello, my friend! Very thorough and detailed solution! Great job! You are the best haha
Thank you! Cheers! You are always a breath of fresh air my friend.
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Answer is 17.Amazing problem,keep making more problems like this.I would be glad to address them.
Excellent Sarit
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Love and prayers from the USA!
Same to you from India ❤️❤️.
Lovely and interesting. Thanks for re energizing my brain. Keep it up please
Thanks dear
You are awesome 👍
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Nice 😉👍👍👍👍👍👍
wondeful👍👍👍👍👍
Thank you Abdellah dear! Cheers!
@PreMath I DO WISH u would explain why u begin where u do and subtracting / adding equations. Especially with system
Nice radical question sir your way of explanation very good anyone can understand easily
So nice of you Sarma.
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Good. thanks
Awesome explanation !
really detailed solution
Nice process
Thanks Souleymane dear
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Awesome ✍️
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Bohoth prasanna hei!
Good job !sir
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Amazing technique.
wow great solution
nice solution sir thank u
Most welcome Nico.
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Amazing
Thanks for recommending me!
Keep watching Aash. This is my gift of education to you!
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@@PreMath thanks you as well
Awesome
Good trick
Please explain why you start with adding the equations together.
@PreMath I DO WISH u would explain why he begins where he does. Especially with systems.
Magnífico
Thank you 🙏
You’re welcome 😊
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Very intrusting sir
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In given relations ,by equality for (x+y) we get
x+y=16...........now , add this two equations then we also get x^2+y^2=18(x+y) then
x^2+y^2+1=(18)(16)+1=289
√x^2+y^2+1=17
Super trick
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👌👌
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You could have plugged 288 (x^2 +y^2 = 288) into the sq rt and come up with 17. I will say in all honestly your way was more eloquent.
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his method of calculating 16.18+1 is better if you are in a math contest where calculator is not allowed, and you sucked at mental math
Super mathematician
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Won't it also be -17? There has to be both right?
Can we prove this by finding and substituting x and y values.. By the equations
X+Y=...
X-Y=...
Add subtraction method sir?
Oh Wow!
good
I wasn't sure that a pair of numbers exist that have a sum of 16 and a sum of squares of 288 but from investigation it appears that one number is approx 16.945 and the other is approx -0.945.
Cool
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@@PreMath also there can be complex number solution!
The solution is that one variable is 8 + ✓(80) and the other is 8 - ✓(80), and these match your estimates.
👍
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Did a similar problem somewhere else. answer 17
but sir how can you subtract eq1 to eq2 without equaling both equetion
But there is no need to square 17 and 1. We know that x^2+y^2= 288, so 288+1=289 square rooted is 17.
I must be the 6 percent then, btw nice solution man
Excellent
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Sir
How can we find the values of x and y plz
I'll explain that one in some other video. That'll be completely different way. Thanks for asking
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Not sure if you got the answer yet but, if you look at the video again, we found out that x+y=16. Thus, y=10-x. Substitute this new y-value in the first equation: x^2 = 17x + (16-x). We will now get to solve a quadratic equation for x: x^2-16x-16=0.
√x^2+y^2+1 is not negative
Because this value is negative then
x,y be negative.And from given equation this isn't possible.
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√x^2+y^2+1=(+17,-17)
You and Presh Talwalker presented this problem BUT both of you got it incorrect: It's not (17+1)(17-1) or vice versa, solve and change the -1 to a +1 on the left side, then take square root of both sides. You are supposed to: MULTIPLY the 16*18 or vice versa first, getting 288, then ADD 1 to BOTH sides, then take the square root of both sides(this is why it is called an equation, meaning both sides have to be balanced in the equation), then solve. This is a simple math problem. Skipping steps gets points deducted in high school. You don't get extra points for skipping steps.
A X al cuadrado más Y elevado al cuadrado súmale 1 y al producto de 18x16 súmale 1 y listo!!!!
X^2 + Y^2 = 18x16; X ^2 + Y^2 + 1 = 18x16 + 1; X^2+ Y^2 + 1 = 289; then 17.
¡Súper!
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It can be solved as x2+y2=18×16=288
X2+y2+1=288+1=289
Square root of 289=17
Eightline shorter
Can -17 be an answer?
Only positive value!
Thanks for asking.
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Why positive values?
I have a different approach...
X²+y²=18(X+y)
√(18(X+y)+1)=z
Z²= 18(X+y)+1
Now Euclid division...a number when divided by 18 leaves r=1 and that number is also a perfect square so the least value of X+y =16 ...
18*16+1=z²
Z=17
y variable
Yep, Got it wrong again. Here is how I started. Arranged both equations 1. x^2 -17x=y 2. y^2-17y=x. Substituted in and didn't get that answer.
Dear Paul, this is a very unique problem. We'll handle it differently. Keep trying my friend.
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x variable
17
Easy problem
Great
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Answer is 17 ??.
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If x is not equal to y, no solution.But if it equal the answer would be 24.01.Check the answer.
x + y = 16
x = ?
17 is the answer
Anser is 17 it was easy peasy not that tough!
Value = 17. I got it thanks
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Ans 17
Cool
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17
y = ?