Question

Giải hpt:

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

Answer 1

\(pt\left(1\right)\Leftrightarrow\left(x-2y\right)\left(x+y+1\right)=0\)

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

*)Xét \(x=2y\Rightarrow pt\left(2\right)\Leftrightarrow4y^2+y^2=1\Leftrightarrow5y^2=1\)

\(\Leftrightarrow y^2=\frac{1}{5}\Leftrightarrow y=\pm\frac{1}{\sqrt{5}}\)\(\Leftrightarrow x=2y=2\cdot\pm\frac{1}{\sqrt{5}}=\pm\frac{2}{\sqrt{5}}\)

*)Xét \(x=-1-y\Rightarrow pt\left(2\right)\Leftrightarrow y^2+2y+1+y^2=1\)

\(\Leftrightarrow2y^2+2y=0\Leftrightarrow2y\left(y+1\right)=0\)\(\Leftrightarrow\left[\begin{matrix}y=0\\y=-1\end{matrix}\right.\)

Answer 2

may quá mất mạng nhưng cx kịp gửi