Question

已知x2+y2-3xy=0求x-y/x+y

Answer 1

因为x^2 y^2-3xy=0 所以x^2 y^2-2xy-xy=0 得出(x-y)^2-xy=0 即(x-y)^2=xy
又因为x^2 y^2-3xy=x^2 y^2 2xy-5xy=0 所以(x y)^2-5xy=0 得出(x y)^2=5xy 则(x-y)^2除以(x y)^2=xy/5xy=1/5 所以(x-y)/(x y)=正负五分之根号五。

Answer 2

x2+y2-3xy=0
(x+y)²=5xy (x-y)²=xy
所以x-y/x+y=±根号（xy/5xy）=±根号1/5

追问

为撒子 (x+y)²=5xy (x-y)²=xy

追答

x2+y2-3xy=0 这个配成完全平方式
x2+y2+2xy-2xy-3xy=0
(x+y)²-5xy=0

同理x2+y2-3xy=0
x2+y2-2xy+2xy-3xy=0
(x-y)²-xy=0
(x-y)²=xy

Answer 3

（x－y）²＝xy （x＋y）²＝5xy x－y／x＋y＝∨5／5