Question

Solve
$(x+2{)}^3=x(x^2-1)$

Answer 1

We have,

${\left(x+2\right)}^3=x\left(x^2-1\right)$

${\left(x+2\right)}^3=x^3-x$

We know that,

${\left(a+b\right)}^3=a^3+b^3+3a^{2}b+3a{b}^2$

$x^3+2^3+3x^2.2+3x{.2}^2$=$x^3-x$

$x^3+8+6x^2+12x$=$x^3-x$

$6x^2+13x+8=0$

$6x^2-3x+16x+8=0$

$3x\left(2x-1\right)+8\left(2x-1\right)=0$

$\left(3x+8\right)\left(2x-1\right)=0$

Hence,

We get $x=\frac{1}{2}x=\frac{-8}{3}$