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-\...")
Solution
Solution by e_power_pi_times_i
![$t = \dfrac{1}{1-\sqrt[4]{2}} = (\dfrac{1}{1-\sqrt[4]{2}})(\dfrac{1+\sqrt[4]{2}}{1+\sqrt[4]{2}}) = (\dfrac{1+\sqrt[4]{2}}{1-\sqrt{2}})(\dfrac{1+\sqrt{2}}{1+\sqrt{2}}) = \dfrac{(1+\sqrt[4]{2})(1+\sqrt{2})}{-1} = \text{(E)}-(1+\sqrt[4]{2})(1+\sqrt{2})$](http://latex.artofproblemsolving.com/c/6/e/c6ede94c008ed200fa9a2ee4f8df9e437a7ff54b.png)
.
