Is it possible to find three numbers,
, none of which is zero or a perfect square, such that
Can You Solve These – David Wells
As 
and 
can’t be perfect squares, let 
and 
where 
and 
are real numbers.
Hence 
and 
.
For the above equation to be possible 
and 
must simplify to the same surd. Because we are looking for one set of numbers, let 
.
Let’s think of some numbers that might work…
or 
, etc.
Let’s try 
and 
We now have 
and 
As 
can’t be a square number, 
can’t be a square number.
Try 
One set of possible numbers are 
and 
.