Question

Giải phương trình ( 2 - m mũ 2 ) . m = - 1

Answer 1

Ta có : \(\left(2-m^2\right)m=-1\)

\(\Leftrightarrow2m-m^3+1=0\)

\(\Leftrightarrow m^3-2m-1=0\)

\(\Leftrightarrow m^3+m^2-m^2-m-m-1=0\)

\(\Leftrightarrow m^2\left(m+1\right)-m\left(m+1\right)-\left(m+1\right)=0\)

\(\Leftrightarrow\left(m+1\right)\left(m^2-m-1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}m=-1\\m=\dfrac{1\pm\sqrt{5}}{2}\end{matrix}\right.\)

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