Question

Solve. (Enter answer as a command-separated list)$\sqrt[3]{2x {}^{2} + 9x - 47} = \sqrt[3]{x {}^{2} + 5x - 2}$

Answer 1

The Solution.

The given equation is

$\sqrt[3]{2x^2+9x-47}=\text{ }\sqrt[3]{x^2+5x-2}$

Raising both sides to the power of 3, we get

$2x^2+9x-47=x^2+5x-2$

Collecting the like terms, we get

$\begin{gathered} 2x^2-x^2+9x-5x-47+2=0 \\ x^2+4x-45=0 \end{gathered}$

Solving quadratically by factorization method, we get

$\begin{gathered} x^2+9x-5x-45=0 \\ x(x+9)-5(x+9)=0 \\ (x+9)(x-5)=0 \end{gathered}$

So,

$\begin{gathered} x+9=0\text{ or x-5=0} \\ x=-9\text{ or x = 5} \end{gathered}$

Therefore, the correct answer is 5 or -9