Vyriešiť x=frac{a^{3}+a^2b^2}{a^2+b^2}

$$x = \frac { a ^ { 3 } + a ^ { 2 } b ^ { 2 } } { a ^ { 2 } + b ^ { 2 } }$$

Riešenie pre b

$$\left\{\begin{matrix}b=\sqrt{\frac{a-x}{x-a^{2}}}|a|\text{; }b=-\sqrt{\frac{a-x}{x-a^{2}}}|a|\text{, }&\left(x<a^{2}\text{ or }x\leq a\right)\text{ and }a\neq 0\text{ and }a\neq 1\text{ and }\left(x>a^{2}\text{ or }x\geq a\right)\text{ and }x\neq a^{2}\\b\in \mathrm{R}\text{, }&x=1\text{ and }a=1\\b\neq 0\text{, }&a=0\text{ and }x=0\end{matrix}\right,$$