Question

tìm x: (x+\(\dfrac{1}{2}\))³=x+\(\dfrac{1}{2}\)

Answer 1

Lời giải:

\(\left(x+\frac{1}{2}\right)^3=x+\frac{1}{2}\)

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

\(\Leftrightarrow \left(x+\frac{1}{2}\right)\left[\left(x+\frac{1}{2}\right)^2-1\right]=0\)

\(\Leftrightarrow \left(x+\frac{1}{2}\right)\left(x+\frac{1}{2}-1\right)\left(x+\frac{1}{2}+1\right)=0\)

\(\Leftrightarrow \left(x+\frac{1}{2}\right)\left(x-\frac{1}{2}\right)\left(x+\frac{3}{2}\right)=0\)

\(\Rightarrow \left[\begin{matrix} x=-\frac{1}{2}\\ x=\frac{1}{2}\\ x=-\frac{3}{2}\end{matrix}\right.\)