One possibility is that both those powers of 25 be equal to 1 so that 1+ 1= 2. In that case we must have and . Adding those 2 equations, 1+ 2(cos x+ cos y)+ 2= 0 or cos x+ cos y= -3/2. From that cos y= -3/2- cos x. You can put that into to get a quadratic equation for cos x and then find x and y.