5-2-1-3-5-2-1-3-2014-

Question Number 182188 by mathlove last updated on 05/Dec/22

{(\sqrt[3]{\sqrt{5} + 2} + \sqrt[3]{\sqrt{5} - 2})}^{2014} = ?

Answered by Frix last updated on 05/Dec/22

\sqrt[3]{2 + \sqrt{5}} = φ \land \sqrt[3]{- 2 + \sqrt{5}} = \frac{1}{φ}

φ + \frac{1}{φ} = \sqrt{5}

{(\sqrt{5})}^{2014} = 5^{1007}

Answered by mnjuly1970 last updated on 05/Dec/22

x^{3} = 2 \sqrt{5} + 3 x \Rightarrow x = \sqrt{5}

a n s w e r = 5^{1007}