Question

Answer 1

\(\Delta=4-\left(6m+9\right)=-6m-5\)

Để pt có 2 nghiệm pb \(-6m-5>0\Leftrightarrow m< -\dfrac{5}{6}\)

Theo Vi et \(\left\{{}\begin{matrix}x_1+x_2=4\left(1\right)\\x_1x_2=6m+9\left(2\right)\end{matrix}\right.\)

Ta có : \(2x_1-x_2=6\)(3) 

Từ (1) ; (3) suy ra : \(\left\{{}\begin{matrix}x_1+x_2=4\\2x_1-x_2=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x_1=\dfrac{10}{3}\\x_2=\dfrac{2}{3}\end{matrix}\right.\)

Thay vào (2) ta được : \(\dfrac{10}{3}.\dfrac{2}{3}=6m+9\Leftrightarrow20=54m+81\Leftrightarrow m=-\dfrac{61}{54}\)