Đề là \(x_1\left(x_1^2-1\right)-x_1\left(8x_2^2+1\right)=5\) hay \(x_2\left(x_1^2-1\right)-x_1\left(8x_2^2+1\right)=5\) hay \(x_2\left(x_1^2-1\right)+x_1\left(8x_2^2-1\right)=5\)
Nhìn đề của bạn thấy nghi ngờ quá
\(\Delta=25-4\left(4-9m\right)>0\Rightarrow36m+9>0\Rightarrow m>-\frac{1}{4}\)
\(\left\{{}\begin{matrix}x_1+x_2=-5\\x_1x_2=4-9m\end{matrix}\right.\)
\(x_1\left(x_1^2-1\right)-x_2\left(8x_2^2-1\right)=5\)
\(\Leftrightarrow x_1^3-8x_2^3-\left(x_1+x_2\right)=5\)
\(\Leftrightarrow x_1^3-8x_2^3+5=5\)
\(\Leftrightarrow x_1^3-8x_2^3=0\Rightarrow x_1^3=\left(2x_2\right)^3\Rightarrow x_1=2x_2\)
Kết hợp Viet: \(\left\{{}\begin{matrix}x_1+x_2=-5\\x_1=2x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}3x_2=-5\\x_1=2x_2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_2=-\frac{5}{3}\\x_1=-\frac{10}{3}\end{matrix}\right.\)
\(x_1x_2=4-9m\Rightarrow4-9m=\frac{50}{9}\Rightarrow m=-\frac{14}{81}\) (t/m)
