Question

giải hệ PT: \(\hept{\begin{cases}\sqrt{3}x-y=1\\5x+\sqrt{2}y=\sqrt{3}\end{cases}}\)

Answer 1

\(\hept{\begin{cases}\sqrt{3}x-y=1\\5x+\sqrt{2}y=\sqrt{3}\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}\sqrt{6}x-\sqrt{2}y=\sqrt{2}\\5x+\sqrt{2}y=\sqrt{3}\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}\left(\sqrt{6}+5\right)x=\sqrt{2}+\sqrt{3}\\\sqrt{3}x-y=1\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{\sqrt{2}+\sqrt{3}}{\sqrt{6}+5}\\\frac{\sqrt{3}\left(\sqrt{2}+\sqrt{3}\right)}{\sqrt{6}+5}-1=y\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{\sqrt{2}+\sqrt{3}}{\sqrt{6}+5}\\y=\frac{-2}{\sqrt{6}+5}\end{cases}}\)

Vậy: Hệ có nghiệm duy nhất thỏa mãn : \(\left(x;y\right)=\left(\frac{\sqrt{2}+\sqrt{3}}{\sqrt{6}+5};\frac{-2}{\sqrt{6}+5}\right)\)

=.= hk tốt!!