Question

Если x+y=xy=6, чему будет равен x3+y3?

Answer 1

$\begin{cases}x+y=6\smallskip\\xy=6\end{cases}\bigskip\\x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\bigskip\\\left(x+y\right)^2=6^2\medskip\\x^2+2xy+y^2=36\medskip\\x^2+y^2=36-2xy\medskip\\x^2+y^2=36-2\cdot 6=36-12=24\bigskip\\x^3+y^3=6\left(24-6\right)=6\cdot 18=108$

Ответ. $108$