Question

Tìm x : x^3 + 27 = -x^2 + 9

Answer 1

\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x-3\right)\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x^2-2x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\\left(x-1\right)^2+5=0\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=-3\)

Answer 2

\(x^3+27=-x^2+9\)

\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x-3\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^2-2x+6\right)=0\)

hay x=-3