Question

已知（x+y）^2=7,(x-y)^2=13,求(1)x^2+y^2 (2）xy

Answer 1

（x+y）^2+(x-y)^2=7+13

x^2+2xy+y^2+x^2-2xy+y^2=20

2(x^2+y^2)=20

x^2+y^2=10

（x+y）^2-(x-y)^2=7-13

[(x+y)+(x-y)][(x+y)-(x-y)]=-6

(2x)(2y)=-6

4xy=-6

xy=-3/2