Well, in this case substituting k = x = h = 1
did happen to work, since
which is false. So k=x=h=1 does produce
a counter-example.
However if the problem had been instead
and you substituted k = x = h = 1
That would have been true, not false. So you would
in that case need to use another number besides 1,
say 2, in order to get a counter-example.
For instance if you substituted k = x = h = 2 in
you get
which is false.
My point is that you may have to substitute other
values for x, h, and k besides 1 in order to find a
counter-example. Never assume that if you get a true
equation, that the given equation is necessarily true.
In fact in some cases you cannot use the same value
for all the variables. Take
If you use the same values for all three variables
you will never get a counter-example.
You'd have to use something like k=1, h=2, and k=3
to get a counter-example.
Edwin