Question

Tìm x và y biết :  \(x+y+13=2\left(2\sqrt{x}+3\sqrt{y}\right)\)

Answer 1

ĐKXĐ: x;y >=0

Ta có : \(x+y+13=2\left(2\sqrt{x}+3\sqrt{y}\right)\)

\(\Leftrightarrow x+y+13=4\sqrt{x}+6\sqrt{y}\)

\(\Leftrightarrow x+y+13-4\sqrt{x}-6\sqrt{y}=0\)

\(\Leftrightarrow\left(x-4\sqrt{x}+4\right)+\left(y-6\sqrt{y}+9\right)=0\)

\(\Leftrightarrow\left(\sqrt{x}-2\right)^2+\left(\sqrt{y}-3\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}\left(\sqrt{x}-2\right)^2=0\\\left(\sqrt{y}-3\right)^2=0\end{cases}\Rightarrow\hept{\begin{cases}x=4\\y=9\end{cases}}\left(TMĐKXĐ\right)}\)