Question

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

Answer 1

(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