Question

Giải hệ pt:

a)\(\left\{{}\begin{matrix}x-\left(1+\sqrt{3}\right)y=1\\\left(1-\sqrt{3}\right)x+y=1\end{matrix}\right.\)

b)\(\left\{{}\begin{matrix}-x-\sqrt{2}y=\sqrt{3}\\\sqrt{2}x+2y=-\sqrt{6}\end{matrix}\right.\)

Answer 1

a: \(\Leftrightarrow\left\{{}\begin{matrix}\left(1-\sqrt{3}\right)x+2y=1-\sqrt{3}\\\left(1-\sqrt{3}\right)x+y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\sqrt{3}\\x=1+\left(1+\sqrt{3}\right)\cdot\left(-\sqrt{3}\right)=-2-\sqrt{3}\end{matrix}\right.\)

b: \(\Leftrightarrow\left\{{}\begin{matrix}-x-\sqrt{2}y=\sqrt{3}\\x+\sqrt{2}y=-\sqrt{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\in R\\x=-\sqrt{3}-y\sqrt{2}\end{matrix}\right.\)