Question

giải cho mik bài 3

Answer 1

3.1. Bạn tự giải

3.2. 

\(\Delta=\left(2m+1\right)^2-4\left(m^2-1\right)=4m+5>0\Rightarrow m>-\dfrac{5}{4}\)

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

\(\left(x_1-x_2\right)^2=x_1-5x_2\)

\(\Leftrightarrow\left(x_1+x_2\right)^2-4x_1x_2=\left(x_1+x_2\right)-6x_2\)

\(\Leftrightarrow\left(-2m-1\right)^2-4\left(m^2-1\right)=-2m-1-6x_2\)

\(\Leftrightarrow4m+5=-2m-1-6x_2\)

\(\Rightarrow6x_2=-6m-6\Rightarrow x_2=-m-1\)

Thay vào \(x_1+x_2=-2m-1\Rightarrow x_1=-m\)

Thay vào \(x_1x_2=m^2-1\Rightarrow-m\left(-m-1\right)=m^2-1\)

\(\Leftrightarrow m=-1\)