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Some Squares Sum Square (
Posted on 20120730
)
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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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 20120731 05:18:05
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