Question

已知x+y=1,x3+y3=100.求x2+y2的值

Answer 1

x3+y3=100

(x+y)(x^2-xy+y^2)=100

因x+y=1

所以

x^2-xy+y^2=100

(x+y)^2-3xy=100

1-3xy=100

xy=-33

x^2+y^2

=(x+y)^2-2xy

=1-2*(-33)

=67