Positive real numbers \(x,y\) satisfy the equations \(x^2 + y^2 = 1\) and \(x^4 + y^4= \frac{17}{18}\). Find \(xy\).
xy = 5/2.
Square both sides of the first equation:
(x2+y2)2 = 12 or x4+ 2(xy)2 + y4 = 1
So: 17/18 + 2(xy)2 = 1
2(xy)2 = 1/18
(xy)2 = 1/36
xy = 1/6 or xy = -1/6
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+87 
