Question

Giải phương trình sau:

(x - 1)³ + (2 - 3x)³  = (1 = 2x)³

Answer 1

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

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

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

\(\Leftrightarrow3\left(x-1\right)\left(2-3x\right)\left(1-2x\right)=0\)

\(\Leftrightarrow x-1=0\) hay \(2-3x=0\) hay \(1-2x=0\)

\(\Leftrightarrow x=1\) hay \(x=\dfrac{2}{3}\) hay \(x=\dfrac{1}{2}\)

-Vậy \(S=\left\{1;\dfrac{2}{3};\dfrac{1}{2}\right\}\)