已知x-y=5 xy=3 求x分之1 - y分之1

1、答案：负七分之五解题：xy=2x+2y代入原式,整理合并同类项即可得出2、如果只考虑在同一平面内,有三条线.如图

x/y=3x=3y(x²+2xy-3y²)/(x²-xy+y²)=(9y²+6y²-3y²)/(9y²-3y²

1/x-1/y=3x-y=-3xy(2x+3xy-2y)/(x-2xy-y)=[2(x-y)+3xy]/[(x-y)-2xy]=(-3xy)/(-5xy)=3/5

∵(x+y)分之xy=3∴xy=3(x+y)∴(-2x+3xy-2y)分之(3x-5xy+3y)=[-2(x+y)+9(x+y)]分之[3(x+y)-15(x+y)]=[7(x+y)]分之[-12(x

根据x+y=5,xy=3,的出（x+y）的平方=19求根号y分之x+根号x分之y可以先求它的平方值\x0d得出式y的平方/x+2倍的xy/根号XY+x的平方/y然后再可并y的平方/x+x的平方/y的出

因为x-y=4xy所以x-2xy-y=2xy2x+3xy-2y=11xyx-2xy-y分之2x+3xy-2y=5.5

xy/(x+y)=2∴xy=2(x+y)(3xy-x-y)/(3x-5xy+3y)=[6(x+y)-x-y]/[3x+3y-10(x+y)]=5(x+y)/[-7(x+y)]=-5/7

因为X+Y分之XY=2,所以XY=2(X+Y)代入后面的分子式得：13（X+Y)/5(X+Y)=13/5

∵x＋y＝5,xy＝3∴x＞0,y＞0√﹙x/y﹚＋√﹙y/x﹚＝√xy/y＋√xy/x＝√xy﹙x＋y﹚/xy＝﹙x＋y﹚/√xy＝5/√3＝5√3/3再问：√xy﹙x＋y﹚/xy怎么化为﹙x＋y﹚

x+y分之xy=2,则xy/(x+y)=2xy=2x+2y(-x+3xy-y)分之(3x-5xy+3y)=(3x-5xy+3y)/(-x+3xy-y)=[3x-5(2x+2y)+3y)/[-x+3(2

(x分之1)+(y分之1)=5（x+y)/xy=5x+y=5xy代入（x+2xy+y)分之(2x-3xy+2y)=7xy分之7xy=1

(y-x)/xy=3y/xy-x/xy=3所以1/x-1/y=3(3x-5xy-3y)/(x-2xy-y)分子分母同时除以xy原式=(3/y-5-3/x)/(1/y-2-1/x)=[3(1/y-1/x

1/X-1/Y=5Y-X=5XY,(X-3XY-Y)/(3X+5XY-3Y)=［-(Y-X)-3XY］/［-3(Y-X)+5XY］=(-8XY)/(-10XY)=4/5.

设1/x-1/y=t(5x+xy-5y)/(x-xy-y)=(1-5(1/x-1/y))/(-1-(1/x-1/y))=(5t-1)/(t+1)至于是1/x-1/y=3还是1/y-1/x=3都差不多

1/x-1/y=(y-x)/xy=2y-x=2xy(3x-5xy-3y)/(-x+3xy+y)={3(x-y)-5xy}/(y-x+3xy)={(-3)*2xy-5xy}/5xy=-11/5

x+y分之xy=2,则xy/(x+y)=2xy=2x+2y(-x+3xy-y)分之(3x-5xy+3y)=(3x-5xy+3y)/(-x+3xy-y)=[3x-5(2x+2y)+3y)/[-x+3(2

1/x-1/y=3(y-x)/xy=3y-x=3xyx-y=-3xy(5x+xy-5y)/(x-xy-y)=[5(x-y)+xy]/[(x-y)-xy]=[5*(-3xy)+xy]/[(-3xy)-x

1/x－1/y＝5,通分得：(y-x)/(xy)＝5,即y－x＝5xy,或写作x－y＝-5xy,代入所求式,得：(3x+5xy-3y)/(x-3xy-y)＝[3(x-y)+5xy]/[(x-y)-3x

1/x-1/y=3(y-x)/xy=3y-x=3xyx-y=-3xy所以原式=[5(x-y)+3xy]/[(x-y)-2xy]=(-15xy+3xy)/(-3xy-2xy)=(-12xy)/(-5xy

∵x分之1-y分之1=3∴y-x=3xy∴x-xy-y分之5x+xy-5y=-4xy分之-4xy=1