Question

Find the general values of $x$ and $y$ which make the following expression a perfect square:
$5x^2+y^2$.

Answer 1

$5x^2+3y^2$

$5x^2=x^2-y^2$

Putting $5mx=n(z+y)$

$nx=m(z-y)$

By cross-multiplication , we get;-

$\frac{x}{2mn}=\frac{y}{{5m}^2-n^2}=\frac{z}{{5m}^2+n^2}$

Hence, $x=2mn,y=5m^2-n^2$ and the hypotenuse is $5m^2+n^2$.