If x= 5 - 5^2/3 - 5^1/3, prove that x^3 - 15x^2 + 60x - 20 = 0.

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x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}

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

15 x^{2} + 60 x - 44 = 0

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

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

5 \frac{1}{3}

5 \frac{2}{3}

\div

\frac{1}{3}

\div

x + 3

\frac{1}{5}

\div

1 \frac{1}{5}

= 7

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

2 x^{3} - 6 x - 5 = 0

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