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Curious Cubic Calculation? (Posted on 2004-10-13) Difficulty: 2 of 5
Show that α=√(7+5√2)+√(7-5√2) is an integer. No calculators or computers allowed!

See The Solution Submitted by Old Original Oskar!    
Rating: 3.8333 (6 votes)

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re: Solution | Comment 5 of 14 |
(In reply to Solution by David Shin)

Haha, oops, the square roots and cubes don't work for some reason.  Here's a better version:

From the equations (1+sqrt(2))^3=(7+5sqrt(2)) and (1-sqrt(2))^3=(7-5sqrt(2)), we deduce that a = (1+sqrt(2)) + (1-sqrt(2)) = 2.

  Posted by David Shin on 2004-10-13 13:33:30
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