For what values of x and y is the following inequality is satisfied:
$\displaystyle x^2y^2+x+y>7$
Give a proof
Do like if y is fixed for example and then solve the second degree equation on x. You calculate delta , see when delta>0 or delta<0 depending on y. At the end you will find your surface. At the end to check you are right, you have to obtain a surface that is symmetric by the straight line y=x, because the equation is invariant by changing x to y.