Question

Tìm tất cả giá trị của x thỏa mãn: \(\left(1-x\right)^3\)+\(\left(3-x\right)^3\)=\(\left(4-2x\right)^3\)

Answer 1

Đặt 1-x=a; 3-x=b

4-2x=1-x+3-x=a+b

\(\left(1-x\right)^3+\left(3-x\right)^3=\left(4-2x\right)^3\)

=>\(a^3+b^3=\left(a+b\right)^3\)

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

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

=>ab(a+b)=0

=>(1-x)(3-x)(4-2x)=0

=>\(\left[{}\begin{matrix}1-x=0\\3-x=0\\4-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\\x=2\end{matrix}\right.\)