Question

cho pt \(x^2-mx+m-7=0\) tìm m để pt có 2 No phân biệt x1,x2 sao cho \(x_1=2x_2+12\)

Answer 1

\(\Delta=m^2-4\left(m-7\right)=\left(m+2\right)^2+24>0;\forall m\)

Kết hợp Viet và đề bài:

\(\left\{{}\begin{matrix}x_1+x_2=m\\x_1-2x_2=12\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}3x_2=m-12\\x_1=2x_2+12\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_2=\frac{m-12}{3}\\x_1=\frac{2m+12}{3}\end{matrix}\right.\)

Mà \(x_1x_2=m-7\Rightarrow\left(\frac{m-12}{3}\right)\left(\frac{2m+12}{3}\right)=m-7\)

\(\Leftrightarrow2m^2-21m-81=0\Rightarrow\left[{}\begin{matrix}m=-3\\m=\frac{27}{2}\end{matrix}\right.\)