Question

giúp mình với ạ, mình giải câu b mãi ko ra uhuhu

Answer 1

Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=-2m+1\\x_1x_2=-2m-7\end{matrix}\right.\)

\(\left(x_1+2x_2\right)\left(x_2+2x_1\right)=3\)

\(\Leftrightarrow2x_1^2+2x_2^2+5x_1x_2=3\)

\(\Leftrightarrow2\left(x_1+x_2\right)^2+x_1x_2=3\)

\(\Leftrightarrow2\left(-2m+1\right)^2+\left(-2m-7\right)=3\)

\(\Leftrightarrow4m^2-5m-4=0\) \(\Rightarrow m=\dfrac{5\pm\sqrt{89}}{8}\)