If x^4 - y^4 = -15 and x^2 - y^2 = -3, what is the value of x^2 + y^2?

Answer 1

x^4-y^4 = (x^2-y^2)(x^2+y^2)
-15 = -3(x^2+y^2)
...

and, of course, x=±1, y=±2