Question

A⁴+b⁴=a²b² ,prove that a⁶+b⁶=0

Answer 1

$a^4+b^4=a^2b^2\\ a^4-a^2b^2+b^4=0\\ a^4-2a^2b^2+b^4+a^2b^2=0\\ (a^2+b^2)^2=-a^2b^2$

The only possible option is that $a^2+b^2=0 \wedge a^2b^2=0$ and this condition is met only when $a=0 \wedge b=0$.

$0^6+0^6=0\\ 0=0$