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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 Hint | Comment 3 of 9 |
There is a very elementary (D2) method for determining the triplet(s) and proving that no further triplets exist.

The method basically involves rearranging the  terms in the first equation and due substitution into the second equation.

It is important in this connection to remember that none of F, G and H can be imaginary numbers.

Edited on July 31, 2012, 2:04 pm
  Posted by K Sengupta on 2012-07-31 05:18:05

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