xy=m,且1/x^2+1/y^2=n.则(x-y)^2=

1/x^2+1/y^2=(x^2+y^2)/m^2=n
所以x^2+y^2=nm^2
(x-y)^2=x^2+y^2-2xy=nm^2-2m

nm^2-2m

n=1/x^2+1/y^2=(x^2+y^2)/(xy)^2
n=[(x-y)^2+2xy]/(xy)^2
n=[(x-y)^2+2m]/m^2

所以 (x-y)^2=n*m^2-2m
=m(nm-2)

1式:xy=m
2式:1/x^2+1/y^2=n
推出 (1/x+1/y)^2-2/xy=n
(x+y/xy)^2-2/xy=n
把xy=m带入 (x+y/m)^2-2/m=n
得式4 (x+y)^2=nm^2+2m

题目 (x-y)^2=(x+y)^2-4xy 把式1和4带入
得答案 (x-y)^2=nm^2-2m