Question

Tìm m để phương trình x^2-(3m-1)x+2m^2-m=0 có nghiệm x1, x2 thỏa mãn x1=x2^2

Answer 1

\(PT\Leftrightarrow\left(x-2m+1\right)\left(x-m\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2m-1\\x=m\end{matrix}\right.\).

+) TH1: \(\left\{{}\begin{matrix}x_1=2m-1\\x_2=m\end{matrix}\right.\Rightarrow m^2=2m-1\Leftrightarrow m=1\).

+) TH2: \(\left\{{}\begin{matrix}x_1=m\\x_2=2m-1\end{matrix}\right.\Rightarrow\left(2m-1\right)^2=m\Leftrightarrow\left(m-1\right)\left(4m-1\right)=0\Leftrightarrow\left[{}\begin{matrix}m=1\\m=\dfrac{1}{4}\end{matrix}\right.\).

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