求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值

问题描述:

求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值

(x+y)^2=324,
x^2+y^2+2xy=324.[1]
(x-y)^2=16
x^2+y^2-2xy=16.[2]
[1]-[2]:
4xy=308
xy=77
[1]+[2]:
2(x^2+y^2)=340
x^2+y^2=170