b. Theo hệ thức Vi-ét ta có:
$\left\{\begin{matrix}x_{1} + x_{2} = -m^{2} - 1\\ x_{1}x{2} = m\end{matrix}\right.$
Do đó
$\dfrac{2x_{1}^{2} - x_{1} + 2x_{2}^{2} - x_{2}}{x_{1}x_{2}} = x_{1}x_{2} + \dfrac{55}{x_{1}x_{2}}$
$\Leftrightarrow \dfrac{2(x_{1}^{2} + x_{2}^{2}) - (x_{1} + x_{2})}{x_{1}x_{2}} = x_{1}x_{2} + \dfrac{55}{x_{1}x_{2}}$
$\Leftrightarrow \dfrac{2(x_{1} + x_{2})^{2} - 4x_{1}x_{2} - (x_{1} + x_{2})}{x_{1}x_{2}} = x_{1}x_{2} + \dfrac{55}{x_{1}x_{2}}$$\Leftrightarrow \dfrac{2(x_{1} + x_{2})^{2} - 4x_{1}x_{2} - (x_{1} + x_{2})}{x_{1}x_{2}} = x_{1}x_{2} + \dfrac{55}{x_{1}x_{2}}$
$\Leftrightarrow \dfrac{2(-m^{2} - 1)^{2} - 4m - (-m^{2} - 1)}{m} = m + \dfrac{55}{m}$
Bạn tự giải tiếp nhé !
