Question

已知x+y=a,xy=b 求x的立方+y的立方 和x的5次方+y的5次方

Answer 1

x²+y²=(x+y)²-2xy=a-b

x³+y³=(x+y)(x²-xy+y²)=a(a-b-b)=a²

x^5+y^5=(x²+y²)(x³+y³)-(xy)²(x+y)=(a-b)a²-b²a=a(a²-ab-b²)