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

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