(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is

If x= 2+2^{2/3}+2^{1/3}

solve

x^{3}-6x^{ 2}+ 6x-2 =0

2. Relevant equations

3. The attempt at a solution

First i tried to substitute the values but its turning out to be really big( and i get quite scared when it turns up like this and so i didn't go any further this way)

then I tried to make a cube of x-1

Like this

x^{3}-1 -3x^{2}+ 3x-3x^{ 2}+3x-1+x^{3}=0

<==>(x-1)^{3}+(x-1)^{3}=x^{3}

<==>2(x-1)^{3}=x^{3}

Well I can't get any further!!

Happy if anyone helps!!

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