Question

Tìm m để phương trình \(\left(x^2-4x\right)^2-3\left(x-2\right)^2+m=0\) có 4 nghiệm phân biệt

 

Answer 1

\(\Leftrightarrow\left[\left(x-2\right)^2-4\right]^2-3\left(x-2\right)^2+m=0\)

\(\left(x-2\right)^2=t\ge0\Rightarrow pt\Leftrightarrow\left(t-4\right)^2-3t+m=0\)

\(\Leftrightarrow t^2-11t+16+m=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\Delta=11^2-4\left(16+m\right)>0\\x_1+x_2=11>0\left(tm\right)\\x_1x_2=16+m>0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< \dfrac{57}{4}\\m< 16\end{matrix}\right.\Leftrightarrow m< \dfrac{57}{4}\)