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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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An observation. | Comment 1 of 9

Taking the coefficients on RHS, 2+3+6, surely it can be no coincidence that 1/2+1/3+1/6=1.

And indeed F=2, G=3, H=6 gives a  solution; 2401=2401.

Are there any more, though!??


  Posted by broll on 2012-07-30 14:16:43
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