Question

Tìm x, y biết:

\(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}=4-\sqrt{x}-\sqrt{y}\)

Answer 1

ĐK: \(x,y>0\)

\(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}=4-\sqrt{x}-\sqrt{y}\)

\(\Leftrightarrow\dfrac{1}{\sqrt{x}}+\sqrt{x}-2+\dfrac{1}{\sqrt{y}}+\sqrt{y}-2=0\)

\(\Leftrightarrow\left(\dfrac{1}{\sqrt{x}}-\sqrt{x}\right)^2+\left(\dfrac{1}{\sqrt{y}}-\sqrt{y}\right)^2=0\)
\(\Rightarrow\)\(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x}}=\sqrt{x}\\\dfrac{1}{\sqrt{y}}=\sqrt{y}\end{matrix}\right.\)\(\)\(\)
\(\Rightarrow\)\(\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)