Question

\(\left(x+2\right)^3-x^3=26\)

Answer 1

\(\left(x+2\right)^3-x^3=26\Leftrightarrow\left(x+2-x\right)\left[\left(x+2\right)^2+x\left(x+2\right)+x^2\right]=26\Leftrightarrow2\left(x^2+4x+4+x^2+2x+x^2\right)=26\Leftrightarrow3x^2+6x+4=13\Leftrightarrow3x^2+6x-9=0\Leftrightarrow x^2+2x-3=0\Leftrightarrow x^2-x+3x-3=0\Leftrightarrow x\left(x-1\right)+3\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\Leftrightarrow\)\(\left[{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)

Vậy S={-3;1}