2010/045) If x + y = 2 and x^3+y^3 = 38,

then what does xy equal?

we know

(x+y)^3 = (x^3+y^3) + 3xy(x+y)

putting value from given conditions


2^3 = 38 + 3xy * 2 or 8 = 38 + 6xy => xy = - 5