Question

Giải phương trình:

\(\dfrac{\left(x+1\right)^3-1}{\left(x-1\right)^3+1}=1\)

Answer 1

\(\dfrac{\left(x+1\right)^3-1}{\left(x-1\right)^3+1}=1\)

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

\(\Leftrightarrow2\cdot\left[\left(x+1\right)^2+\left(x+1\right)\cdot\left(x-1\right)+\left(x-1\right)^2\right]-2=0\)

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

\(\Leftrightarrow3x^2-1=0\)

\(\Leftrightarrow3x^2=1\)

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

\(\Leftrightarrow x=\dfrac{1}{\sqrt[]{3}}\)

vây..............