giai he pt

L

lp_qt

ta thấy $x=0;y=0$ ko là nghiệm của hệ

$\left\{\begin{matrix} \sqrt{x}(1+\dfrac{12}{3x+y})=2 & \\ \sqrt{y}(1-\dfrac{12}{3x+y})=6 & \end{matrix}\right.$

\Leftrightarrow $\left\{\begin{matrix}1+\dfrac{12}{3x+y}=\dfrac{2}{\sqrt{x}} & \\
1-\dfrac{12}{3x+y}=\dfrac{6}{\sqrt{y}} & \end{matrix}\right.$

\Leftrightarrow $\left\{\begin{matrix}1=\dfrac{1}{\sqrt{x}}+\dfrac{3}{\sqrt{y}} & \\
\dfrac{12}{3x+y}=\dfrac{1}{\sqrt{x}}-\dfrac{3}{\sqrt{y}} & \end{matrix}\right.$

\Rightarrow $\dfrac{12}{3x+y}=(\dfrac{1}{\sqrt{x}}-\dfrac{3}{\sqrt{y}}).(\dfrac{1}{\sqrt{x}}+\dfrac{3}{\sqrt{y}})$

\Leftrightarrow $\dfrac{12}{3x+y}=\dfrac{1}{x}-\dfrac{9}{y}$

\Leftrightarrow $\dfrac{12}{3x+y}=\dfrac{y-9x}{xy}$

tìm mối quan hệ giữa $x;y$
 
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