Question

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

Answer 1

The solution to the equation is x = ± 17

Solving quadratic equation involving surds.

To solve the equation we need to follow a step-by-step approach below. The first thing to do in this question is to subtract 5 from both sides of the equation.

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

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

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

The next thing to do is to take the cube root of the both sides.

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

`x^2 - 9=8`

`x^2 =8+9`

`x =\pm √(17)`

The complete question.

Solve for x in the equation
`5 - \sqrt[3]{(x^2-9)}=7`