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

1 Answer

5 votes

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

User Nicasio
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