Cho hpt x/a+y/b=căn 2
Và 2x/a+3y/b=-1
Tìm a, b để hpt có Nghiệm (x, y) =(1,1)
Thay x = 1; y = 2 vào HPT ta có:
[tex]\left\{\begin{matrix} \frac{1}{a}+\frac{1}{b}=\sqrt{2} & \\ \frac{2}{a}+\frac{3}{b}=-1 & \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} \frac{2}{a}+\frac{2}{b}=2\sqrt{2} & \\ \frac{2}{a}+\frac{3}{b}=-1& \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} \frac{1}{b}=-2\sqrt{2}-1 & \\ \frac{1}{a}=1+3\sqrt{2}& \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} b=\frac{1-2\sqrt{2}}{7} & \\ a=\frac{-1+3\sqrt{2}}{17} & \end{matrix}\right.[/tex]