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Some Squares Sum Square (Posted on 2012-07-30) Difficulty: 2 of 5
Determine all possible non zero real triplet(s) (F, G, H) that satisfy the following system of equations:

(7F)2 + (7G) 2 + (7H) 2 = (2F + 3G + 6H) 2 , and :

1/F + 1/G + 1/H = 1

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re(2): Solution (spoiler) | Comment 8 of 9 |
(In reply to re: Solution (spoiler) by Harry)

Very nice proof, but actually there is a much simpler solution.

Just rearrange the terms of the first equation, and express the same as the sum of squares of three linear expressions and, everything else will then fit in. (Note the D2 rating.)

Edited on August 1, 2012, 2:29 pm
  Posted by K Sengupta on 2012-08-01 14:27:22

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