Find all triplets(x,y,z) of integers such that
1/x² + 1/y² + 1/z² = 2/3

              x      y      z
   N        2       2      2
  Nē        4       4      4
1/Nē     0.25  0.25  0.25   sum= 0.75

              x      y      z
   N        2       2      3
  Nē        4       4      9
1/Nē     0.25  0.25  0.111   sum= 0.611

In the first table above, if x=y=z=2 [N] the the sum is greater than 2/3.

In the second table, just incrementing one value by 1 gives a sum which is less than 2/3.

Since there are no integers between 2 and 3 then there is no way to arrive at 2/3 for the proposal offered.

Edited on December 4, 2012, 9:00 pm

Posted by brianjn on 2012-12-04 20:31:20