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Question Number 14658 by tawa tawa last updated on 03/Jun/17

Given that :

x = {(\sqrt{2} + 1)}^{1 / 3} - {(\sqrt{2} - 1)}^{1 / 3}

Show that, x^{3} + 3 x = 2

Answered by Tinkutara last updated on 03/Jun/17

x^{3} = \sqrt{2} + 1 - \sqrt{2} + 1 - 3 (1) (x)

[Using {(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)]

x^{3} + 3 x = 2

Commented by tawa tawa last updated on 03/Jun/17

God bless you sir .