+965 Let x and y be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?
+410 x3+y3=(x+y)(x2−xy+y2).
5=2(x2−xy+y2)
x2−xy+y2=52
Because x2−xy+y2=(x+y)2−3xy
(x+y)2−3xy=52.
22−3xy=52
−3xy=−32
xy=12
x2+y2=(x+y)2−2xy=4−1=3.
So x2+y2 is 3.
