Question

Giải hệ pt

\(\left\{{}\begin{matrix}x\sqrt{x}-3x\sqrt{y}+3y\sqrt{x}-y\sqrt{y}=0\\x^2-2\sqrt{xy}+y=0\end{matrix}\right.\)

Answer 1

ĐKXĐ: ...

\(x\sqrt{x}-3x\sqrt{y}+3y\sqrt{x}-y\sqrt{y}=0\)

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

\(\Leftrightarrow\sqrt{x}=\sqrt{y}\Leftrightarrow x=y\)

Thay xuống dưới:

\(x^2-2x+x=0\Leftrightarrow x^2-x=0\)

\(\Rightarrow\left[{}\begin{matrix}x=y=0\\x=y=1\end{matrix}\right.\)