Question

các bạn giúp với:

1/\(\left\{{}\begin{matrix}x-2y-\sqrt{xy}=0\\\sqrt{x-1}+\sqrt{4y-1}=2\end{matrix}\right.\)

2/\(\left\{{}\begin{matrix}2x^3-9y^3=\left(x-y\right).\left(2xy+3\right)\\\left(x^2+y^2\right)=3+xy\end{matrix}\right.\)

Answer 1

1/

\(\left(1\right)\Leftrightarrow x-2\sqrt{xy}+\sqrt{xy}-2y=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=y=0\\x=4y\end{matrix}\right.\)

2/ thay \(3=x^2+y^2-xy\) vào (1) ta được

\(2x^3-9y^3=\left(x-y\right)\left(x^2+y^2+xy\right)\)

\(\Leftrightarrow2x^3-9y^3=x^3-y^3\)

\(\Leftrightarrow x^3-8y^3=0\)

\(\Leftrightarrow\left(x-2y\right)\left(x^2+2xy+4y^2\right)=0\)

\(\Leftrightarrow x=2y\)