Question

What are the solutions to this equation?

1
-1
√17
-√17
There are no solutions.

Answer 1

`5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm√(1)=x\implies \pm 1 = x`

Answer 2

1 and -1

Explanation:

`5 - \sqrt[3]{( {x}^(2) - 9 } = 7`

`- \sqrt[3]{( {x}^(2) - 9} = 7 - 5`

`- \sqrt[3]{( {x}^(2) - 9} = 2`

`\sqrt[3]{( {x}^(2) - 9} = - 2`

Cube both sides of the equation:

`{x}^(2) - 9 = { - 2}^(3)`

`{x}^(2) - 9 = - 8`

`{x}^(2) = - 8 + 9`

`{x}^(2) = 1`

`{x}^(2) - 1 = 0`

`(x - 1)(x + 1) = 0`

`x = 1 \: \: or \: \: x = - 1`