Kaya Renger Coordinator
29/09/2017 at 20:23-
\(x^2+102=y^2\Rightarrow y^2-x^2=102\Rightarrow\left(y-x\right)\left(y+x\right)=102\)
We have : y + x = (y - x) + 2x, so :
- If y - x is odd, then y + x is odd and (y - x)(y + x) is odd
(asburd since 102 is even)
- If y - x is even, then y + x is even and \(\left(y-x\right)\left(y+x\right)⋮4\)
(asburd since \(102⋮̸\)\(4\))
So, the equation has no solution
Selected by MathYouLike -
Ngô Tấn Đạt 29/09/2017 at 20:37\(x^2+102=y^2\\ \Rightarrow y^2-x^2=102\\ \Rightarrow\left(y-x\right)\left(y+x\right)=102\\ \)
