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Question Number 157007 by Armindo last updated on 18/Oct/21

Commented by Armindo last updated on 18/Oct/21

I need help, for to solve This exercice.

Answered by TheHoneyCat last updated on 21/Oct/21

$$\frac{1}{{}^4\sqrt{2}{+}^4\sqrt{4}{+}^4\sqrt{8}+2}$$$$=\frac{1}{2^{1/4}+4^{1/4}+8^{1/4}+2}$$$$=\frac{1}{2^{1/4}+2^{2/4}+2^{3/4}+2^{4/4}}$$$$={\left(\underset{k=1}{\sum ^4}{\left(2^{1/4}\right)}^k\right)}^{-1}$$$$={\left(2^{1/4}\frac{2^{4/4}-1}{2^{1/4}-1}\right)}^{-1}=\frac{\sqrt[4]{2}-1}{\sqrt[4]{2}}\approx 0.2$$$$$$$$thesecondformulahasnosimplification...$$

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