Question

x³ - 8 = x² + 2x + 4

Answer 1

Ta có: \(x^3-8=x^2+2x+4\)

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

\(\Leftrightarrow\left(x^2+2x+4\right)\left(x-2-1\right)=0\)(1)

Ta có: \(x^2+2x+4\)

\(=x^2+2x+1+3\)

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

Ta có: \(\left(x+1\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+1\right)^2+3\ge3>0\forall x\)

hay \(x^2+2x+4>0\forall x\)(2)

Từ (1) và (2) suy ra x-3=0

hay x=3

Vậy: S={3}