Question

$$( a ^ { 2 } + b ^ { 2 } ) ^ { 3 } = ( a ^ { 3 } + b ^ { 3 } ) ^ { 2 }$$

Solve for a

$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$

Solve for b

$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$