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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(2): Solution | Comment 11 of 14 |
(In reply to re: Solution by David Shin)

Hi David, your starting statement

(1+sqrt(2))^3=(7+5sqrt(2)) and (1-sqrt(2))^3=(7-5sqrt(2)) was a bit of a leap for me.  But I managed to figure out that...

7+5sqrt(2) = (3+2sqrt(2))(1+sqrt(2))

= (1+sqrt(2))^3 and then I understood.  Thanks for the help. 

  Posted by Nosher on 2004-10-14 02:02:19
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