How do you solve root3(2x^3 - 24) = -x and find any extraneous solutions?

1 Answer
Jun 27, 2016

Cube both sides.

Explanation:

(root(3)(2x^3 - 24))^3 = (-x)^3

2x^3 - 24 = -x^3

3x^3 = 24

x^3 = 8

x = 2

Checking in the original equation:

root(3)(2(2)^3 - 24 )=^? -2

root(3)(-8) = -2

Therefore, out solution set is {x = 2}.

Hopefully this helps!