已知x+y=10,x^3+y^3=400,求x^2+y^2
问题描述：
已知x+y=10,x^3+y^3=400,求x^2+y^2
答
x^3+y^3=(x+y)(x^2-xy+y^2)
=(x+y)[(x+y)^2-3xy]=400
10(100-3xy)=400
xy=20
x^2+y^2
=(x+y)^2-2xy
=100-40
=60