Given d = (((2+ (√5)))^(1/3) /(1+(√5))) then d^3 −4d^2 +8d −2 =?


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Question Number 194900 by cortano12 last updated on 19/Jul/23

$G i v e n d = \frac{\sqrt[3]{2 + \sqrt{5}}}{1 + \sqrt{5}}$ $t h e n d^{3} - 4 d^{2} + 8 d - 2 = ?$
	Answered by Frix last updated on 19/Jul/23

	$d^{3} = \frac{2 + \sqrt{5}}{{(1 + \sqrt{5})}^{3}} = \frac{2 + \sqrt{5}}{8 (2 + \sqrt{5})} = \frac{1}{8} \Leftrightarrow d = \frac{1}{2}$ $\Rightarrow answer is \frac{9}{8}$
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