Question

\(\left(x^2-3x+2\right)^3+\left(-x^2+x+1\right)^3+\left(2x-3\right)^3=0\)

Answer 1

Đặt \(\left\{{}\begin{matrix}x^2-3x+2=a\\-x^2+x+1=b\\\end{matrix}\right.\) \(\Rightarrow2x-3=-\left(a+b\right)\)

Pt trở thành:

\(a^3+b^3-\left(a+b\right)^3=0\)

\(\Leftrightarrow\left(a+b\right)^3-3ab\left(a+b\right)-\left(a+b\right)^3=0\)

\(\Leftrightarrow ab\left(a+b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\\a+b=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-3x+2=0\\-x^2+x+1=0\\2x-3=0\end{matrix}\right.\)