# Thread: Solution to Cubic

1. ## Solution to Cubic

Given that -
3^1/3 + 3^-1/3 = x

Prove that -
3x^3 - 9x - 10 = 0

My friend suggested something like taking 3^1/3 as 'a'.

2. Originally Posted by Ruler of Hell
Given that -
3^1/3 + 3^-1/3 = x

Prove that -
3x^3 - 9x - 10 = 0

My friend suggested something like taking 3^1/3 as 'a'.
Cube the first equation:

x^3 = 3 + 3*3^{2/3}*3^{-1/3} + 3*3^{1/3}*3^{-2/3} + 1/3

Now multiply through by 3:

3*x^3 = 10 + 9*[3^{1/3} + 3^{-1/3}] = 10 + 9*x

rearrange and:

3x^3 - 9x - 10 = 0

RonL