usun niewymiernosc z mianownika1 / ( 2^(1/6) + 2^(1/4) + 2^(1/2).... Question from @krzys3009

krzys3009 @krzys3009

September 2018 2 41 Report

usun niewymiernosc z mianownika

1 / ( 2^(1/6) + 2^(1/4) + 2^(1/2)

nico112

Albo ja czegoś nie rozumiem albo ty coś źle przepisałeś bo nie widzę niewymierności którą można usunąć ;-)

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matliber

$\frac{1}{2^{\frac{1}{6}} + 2^{\frac{1}{4}} + 2^{\frac{1}{2}}} = \frac{1}{\sqrt[6]{2} + \sqrt[4]{2} + \sqrt{2}} = \frac{\sqrt{2}}{\sqrt[5]{2} + \sqrt[3]{2} +{2}} = \frac{2}{\sqrt[4]{2} + \sqrt{2} + 2\sqrt{2}} = \frac{2}{\sqrt[4]{2} + 3\sqrt{2}} = \frac{2\sqrt{2}}{\sqrt[3]{2} +{6}} = \frac{4}{\sqrt{2} + 6\sqrt{2} = \frac{4\sqrt{x}}{{2}+{12}} = \frac{4\sqrt{x}}{{14}} = \frac{2\sqrt{x}}{{7}}$

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