|
|
a.
Điều kiện: $x,y\ge0$.
Hệ đã cho tương đương với:
$\left\{\begin{array}{l}x\sqrt x-y\sqrt y=\sqrt x+8\sqrt y\\x-y=5\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}5(x\sqrt x-y\sqrt y)=(\sqrt x+8\sqrt y)(x-y)\\x-y=5\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}4x\sqrt x-8x\sqrt y+y\sqrt x+3y\sqrt y=0\\x-y=5\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}(\sqrt x-\sqrt y)(2\sqrt x-3\sqrt y)(2\sqrt x+\sqrt y)=0\\x-y=5\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}4x=9y\\x-y=5\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x=9\\y=4\end{array}\right.$
|