+294 Let x and y be complex numbers. If $x + y =2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?
+399 \(x^3+y^3+(x+y)(x^2-xy+y^2)=(x+y)(x^2+y^2-\frac{(x+y)^2-x^2-y^2}{2}) \)
\(\text{set} \,x^2+y^2=a\)
\(5=(2)(a-\frac{4-a}{2})\)
\(a=x^2+y^2=3 \)
.
+37147 x + y = 2 then ( x + y)^2 = 4 and (x+y)^3 = 8
x^2 + y^2 + 2xy = 4
(x+y)^3 =8 = x^3 + y^3 + 3xy^2 + 3x^2y = x^3 + y^3 + 3xy ( x + y) sub in for x+ y and x^3 + y^3
8 = 5 + 6 xy
3 = 6 xy
1/2 = xy Now sub in to the red equation
x^2 + y^2 + 2 ( 1/2) = 4
x^2 + y^2 = 3
