SOLUTION: If {{{ x= sqrt(pq) }}} and {{{ y = (1/2) (p+q)}}}. Prove {{{x<y}}}

The other tutor is right, so for the statement to be true, we must
change the conclusion from  to 

But that's not all we have to change.

The statement is also not true if p=-1, q=-9

For in that case  
and  and x>y

The statement is also not true if p=0, q=-2

For in that case  
and  and x>y

Also by symmetry it is not true if p=-2, q=0

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So we must change your statement to something that is always true:

If , , , , prove 



So what we are to prove becomes

If  and . Prove 

To prove  is the same as proving 

Let  and 

Then  and 

Then what we are to prove becomes:

If  and . Prove 

So we consider 




With the inclusion in the premise than p and q are non-negative and
in the conclusion that  we have proved the statement. 

Edwin