Positive real numbers x and y satisfy the equations x^2 + y^2 = 1 and x^4 + y^4 = 5/8. Find xy.
x^2 +y^2 = 1
Square both sides
x^4 + 2(xy)^2 + y^4 = 1
Subbing in we have
5/8 + 2(xy)^2 = 1
2(xy)^2 = 1 - 5/8
2(xy)^2 = 3/8
(xy)^2 = 3/16
xy = sqrt (3) / 4
