Question

Answer 1

Δ=(-6)^2-4(6m-m^2)

=36-24m+4m^2=(2m-6)^2>=0

=>Phương trình luôn cóhai nghiệm là \(\left\{{}\begin{matrix}x_1=\dfrac{6-\sqrt{\left(2m-6\right)^2}}{2}=\dfrac{6-2m+6}{2}=\dfrac{12-2m}{2}=6-m\\x_2=\dfrac{6+\sqrt{\left(2m-6\right)^2}}{2}=\dfrac{6+2m-6}{2}=m\end{matrix}\right.\)

x2=x1^3-8x1

=>m=x1(x1^2-8)

=>m=(6-m)(m^2-12m+36-8)

=>m=(6-m)(m^2-12m+28)

=>m=6m^2-72m+168-m^3+12m^2-28m

=>m=-m^3+18m^2-100m+168

=>m^3-18m^2+101m-168=0

=>\(m\in\left\{3;8;7\right\}\)