Positive real numbers x, y satisfy the equations x^2 + y^2 = 1 and x^4 + y^4 = 17/19. Find xy.
x^2 + y^2 = 1 square both sides
x^4 + 2x^2y^2 + y^2 = 1
(x^4 + y^4) + 2(xy)^2 =1
(17/19) + 2(xy)^2 = 1
2(xy)^2 = 1 - 17/19
2(xy)^2 = 2/19 divide through by 2
(xy)^2 = 1/19 take the positive root
xy = sqrt (1/19) = sqrt (19) / 19
