Answer
Proven
Work Step by Step
We have to prove $c^{2} = a^{2} + b^{2}$
on putting given values
$ a^{2} + b^{2 }= (p^{2}-q^{2})^{2} +(2pq)^{2}$
$= p^{4}+ q^{4}-2p^{2}q^{2}+4p^{2}p^{2}$
$= p^{4}+ q^{4}+2p^{2}q^{2}$
$=( p^{2}+q^{2})^{2}$
$= c^{2}$
hence proved
