Question

Tìm x bt

(x+1)^3 +(x+2)^3-(2x +3)^3 =0

Answer 1

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

\(\Leftrightarrow\left(2x+3\right)\left(x^2+2x+1-x^2-3x-2+x^2+4x+4\right)=\left(2x+3\right)^3\)

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

\(\Leftrightarrow\left(2x+3\right)\left(4x^2+12x+9-x^2-3x-3\right)=0\)

\(\Leftrightarrow\left(2x+3\right)\left(3x^2+9x+6\right)=0\)

\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=-1\\x=-2\end{matrix}\right.\)