Clearly for two quadratic equations x^2+m*x+n=o and x^2+m'*x+n'=o to have identical couples of roots m must be equal to m' and n=n'.

In our case A=B.

So x1+x2=A and x1*x2=A

The above set has only one solution in integers: A=B=4: x1=x2=2.

*'Prove that there are no others."-*

* *AFTER FINDING **ALL **SOLUTIONS this is an unnecessary/redundant demand and should be avoided in the future.

n.b. please see my next comment

*Edited on ***October 18, 2016, 7:33 pm**