Question

\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y+9}=9\\\sqrt{y}+\sqrt{x+9}=9\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(x,y\ge0\)

Từ hệ pt trên suy ra \(\sqrt{x}+\sqrt{y+9}=\sqrt{y}+\sqrt{x+9}\Leftrightarrow x+y+9+2\sqrt{xy+9x}=x+y+9+2\sqrt{yx+9y}\Leftrightarrow2\sqrt{xy+9x}=9+2\sqrt{xy+9y}\Leftrightarrow x=y\)

Vậy hệ pt thành \(\sqrt{x}+\sqrt{x+9}=9\Leftrightarrow2x+9+2\sqrt{x^2+9x}=81\Leftrightarrow2\sqrt{x^2+9x}=72-2x\)

( đk : x \(\le\) 36, y \(\le36\))

\(\Leftrightarrow4\left(x^2+9x\right)=5184-288x+4x^2\Leftrightarrow324x=5184\Leftrightarrow x=16\) (tmđk)