\(\Leftrightarrow4^{\left(x-1\right)^2}-2m.2^{\left(x-1\right)^2}+3m-2=0\)
Đặt \(2^{\left(x-1\right)^2}=t\ge1\)
\(\Rightarrow f\left(t\right)=t^2-2m.t+3m-2=0\) (1)
Pt có 4 nghiệm pb khi (1) có 2 nghiệm thỏa mãn \(t_1>t_2>1\)
\(\Rightarrow\left\{{}\begin{matrix}\Delta'=m^2-\left(3m-2\right)>0\\f\left(1\right)=1-2m+3m-2>0\\\dfrac{t_1+t_2}{2}=m>1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m>2\\m< 1\end{matrix}\right.\\m>1\\m>1\end{matrix}\right.\) \(\Rightarrow m>2\)
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