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1977 AHSME Problems/Problem 7

Revision as of 12:10, 18 November 2016 by E power pi times i (talk | contribs) (Created page with "==Solution== Solution by e_power_pi_times_i <math>t = \dfrac{1}{1-\sqrt[4]{2}} = (\dfrac{1}{1-\sqrt[4]{2}})(\dfrac{1+\sqrt[4]{2}}{1+\sqrt[4]{2}}) = (\dfrac{1+\sqrt[4]{2}}{1-\...")
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Solution

Solution by e_power_pi_times_i

$t = \dfrac{1}{1-\sqrt[4]{2}} = (\dfrac{1}{1-\sqrt[4]{2}})(\dfrac{1+\sqrt[4]{2}}{1+\sqrt[4]{2}}) = (\dfrac{1+\sqrt[4]{2}}{1-\sqrt{2}})(\dfrac{1+\sqrt{2}}{1+\sqrt{2}}) = \dfrac{(1+\sqrt[4]{2})(1+\sqrt{2})}{-1} = \text{(E)}-(1+\sqrt[4]{2})(1+\sqrt{2})$.

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