已知x+y=a,xy=b,求(x-y)的平方,(x-y)²,x²+y²,x²-xy+y²的值

问题描述:

已知x+y=a,xy=b,求(x-y)的平方,(x-y)²,x²+y²,x²-xy+y²的值

(x-y)^2=(x+y)^2-4xy=a^2-4b
x²+y²=(x+y)^2-2xy=a^2-2b
x²-xy+y²=(x+y)^2-3xy=a^2-3b

1、(x-y)²=(x+y)²-4xy=a²-4b
2、x²+y²=(x+y)²-2xy=a²-2b
3、x²-xy+y²=(x²+y²)-xy=a²-2b-b=a²-3b