Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix}
\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(1)\\
(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)=35\end{matrix}\right.\)
\(\Rightarrow 35\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)\)
\(\Leftrightarrow (\sqrt{x}+\sqrt{y}))(30x-65\sqrt{xy}+30y)=0\)
Nếu $\sqrt{x}+\sqrt{y}=0$ thì từ $(1)$ suy ra $\sqrt{xy}.0=30$ (vô lý)
Nếu $30x-65\sqrt{xy}+30y=0$
$\Leftrightarrow 6x-13\sqrt{xy}+6y=0$
$\Leftrightarrow (2\sqrt{x}-3\sqrt{y})(3\sqrt{x}-2\sqrt{y})=0$
$\Rightarrow \sqrt{x}=\frac{3}{2}\sqrt{y}$ hoặc $\sqrt{x}=\frac{2}{3}\sqrt{y}$
Thay lần lượt từng TH vào $(1)\Rightarrow (x,y)=(9,4); (4,9)$
Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix}
\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(1)\\
(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)=35\end{matrix}\right.\)
\(\Rightarrow 35\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)\)
\(\Leftrightarrow (\sqrt{x}+\sqrt{y}))(30x-65\sqrt{xy}+30y)=0\)
Nếu $\sqrt{x}+\sqrt{y}=0$ thì từ $(1)$ suy ra $\sqrt{xy}.0=30$ (vô lý)
Nếu $30x-65\sqrt{xy}+30y=0$
$\Leftrightarrow 6x-13\sqrt{xy}+6y=0$
$\Leftrightarrow (2\sqrt{x}-3\sqrt{y})(3\sqrt{x}-2\sqrt{y})=0$
$\Rightarrow \sqrt{x}=\frac{3}{2}\sqrt{y}$ hoặc $\sqrt{x}=\frac{2}{3}\sqrt{y}$
Thay lần lượt từng TH vào $(1)\Rightarrow (x,y)=(9,4); (4,9)$
Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix}
\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(1)\\
(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)=35\end{matrix}\right.\)
\(\Rightarrow 35\sqrt{xy}(\sqrt{x}+\sqrt{y})=30(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)\)
\(\Leftrightarrow (\sqrt{x}+\sqrt{y}))(30x-65\sqrt{xy}+30y)=0\)
Nếu $\sqrt{x}+\sqrt{y}=0$ thì từ $(1)$ suy ra $\sqrt{xy}.0=30$ (vô lý)
Nếu $30x-65\sqrt{xy}+30y=0$
$\Leftrightarrow 6x-13\sqrt{xy}+6y=0$
$\Leftrightarrow (2\sqrt{x}-3\sqrt{y})(3\sqrt{x}-2\sqrt{y})=0$
$\Rightarrow \sqrt{x}=\frac{3}{2}\sqrt{y}$ hoặc $\sqrt{x}=\frac{2}{3}\sqrt{y}$
Thay lần lượt từng TH vào $(1)\Rightarrow (x,y)=(9,4); (4,9)$
