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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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Solution I way I see it | Comment 7 of 14 |

***Oh well, I got gibberish too but I ain't fixing it because it isn't anything new***

 

Each of the numbers in the cube roots must be the cubes of relatively simple numbers with 2 in them.  If one has a positive 2 term and the other its opposite they will cancel out on adding.

Amazing to me was that I found them on my first try:

(1+2) = 7+52

(1-2) = 7-52

(1+2) + (1-2) = 2

a=2 which is an integer

-Jer

Edited on October 13, 2004, 4:07 pm
  Posted by Jer on 2004-10-13 16:03:57

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