Question

Giải hệ phương trình:
\(\left\{{}\begin{matrix}15x=y-5\\16x=y+3\end{matrix}\right.\) \(\left\{{}\begin{matrix}\left(\sqrt{2}+\sqrt{3}\right)x-y\sqrt{2}=\sqrt{2}\\\left(\sqrt{2}+\sqrt{3}\right)x+y\sqrt{3}=-\sqrt{3}\end{matrix}\right.\)
Giúp mình với mình cần gấp!!!

Answer 1

\(\left\{{}\begin{matrix}15x=y-5\\16x=y+3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}15x=y-5\\x=8\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=8\\y=125\end{matrix}\right.\)

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{y\sqrt{2}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\\y=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-24+10\sqrt{6}\\y=5-2\sqrt{6}\end{matrix}\right.\)