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 + 2(xy)^2 + y^4) = 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 both sides by 2
(xy)^2 = 1 /19
xy = sqrt (1/19) = sqrt (19) / 19
