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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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re: An observation. | Comment 2 of 9 |
(In reply to An observation. by broll)

When I looked at this initially I wondered about "non zero real triplet(s)".

I did consider negatives, -2, -3 and -6.  That gives the appropriate 2401=2401 for the first equation but leaves us with a -1 for the second.

Having one or two negatives, and then trying to equate to 1 in the second equation creates an imbalance in the first.

From my spreadsheet I determine F=2, G=3 and H=6.

  Posted by brianjn on 2012-07-30 23:08:45

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