已知1/x+1/y=1/x+y 则y/x+x/y的值

(x+y)2=xy
所以x/y+y/x=(x2+y2)/xy=((x+y)2-2xy)/xy=-1

1/x+1/y=(x+y)/xy=1/(x+y)
xy=(x+y)2=x2+2xy+y2
x2+xy+y2=0
xy=-(x2+y2)
y/x+x/y=(y2+x2)/xy=-xy/xy=-1

1/x+1/y=y/xy+x/xy=x+y/xy,x+y/xy=1/x+y,因为内项积等于外项积,所以xy=(x+y)^2
y/x+x/y=y^2/xy+x^2/xy=x^2+y^2/xy
xy=(x+y)^2=x^2+2xy+y^2,-xy=x^2+y^2,x^2+y^2/xy=-x^2+y^2/-xy=-1