Question

Giải pt\(\dfrac{x^3+8}{2}=\left(\dfrac{x}{2}+1\right)^3\)

Answer 1

\(\Leftrightarrow\dfrac{x^3+8}{2}=\dfrac{\left(x+2\right)^3}{8}\)

\(\Leftrightarrow4x^3+32=\left(x+2\right)^3\)

\(\Leftrightarrow4\left(x+2\right)\left(x^2-2x+4\right)=\left(x+2\right)^3\)

\(\Leftrightarrow\left(x+2\right)\left(4x^2-8x+16\right)-\left(x+2\right)^3=0\)

\(\Leftrightarrow\left(x+2\right)\left(4x^2-8x+16-x^2-4x-4\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(3x^2-12x+12\right)=0\)

\(\Leftrightarrow3\left(x+2\right)\left(x-2\right)^2=0\)

hay \(x\in\left\{2;-2\right\}\)