已知x y =1 xy =5分之1,求(x的平方-1)(x的平方-1)

令F（XY）=1/XY+XY,当XY=1的时候,F（XY)=2,最小.（可由函数图形象得出）.XY趋于正无穷大的时候F(XY)趋于正无穷大,XY无限趋于零的时候F(XY)趋于正无穷大.所以XY越接近1

解1/x+1/y=5即(y+x)/xy=5∴y+x=5xy∴(2x+3xy+2y)/(x-2xy+y)=[2(x+y)+3xy]/[(x+y)-2xy]=[2×5xy+3xy]/(5xy-2xy)=(

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

解(x+1)平方+/y-1/=0∴x+1=0,y-1=0∴x=-1,y=1∴2(xy-5xy平方)-(3xy平方-xy)=(2xy+xy)+(-10xy平方-3xy平方)=3xy-13xy平方=3×(

3xy-[2xy-2(xy-2分之3xy)+xy]+3xy=6xy-[2xy-2xy+3xy+xy)=6xy-4xy=2xy=2×3×3分之1=2

1/x+1/y=(x+y)/(xy)=5x+y=5xy(2x-3xy+2y)/(x+2xy+y)=(2*5xy-3xy)/(5xy+2xy)=(10-3)/(5+2)=1

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

1.已知x+y=-4,xy=3,求5(xy/2+2y)+[6x-(2xy+y-3x)]的值5(xy/2+2y)+[6x-(2xy+y-3x)]=5xy/2+10y+6x-2xy-y+3x=xy/2+9

(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

因1/x+1/y=5(x+2xy+y)/(2x-3xy+2y)上下同乘以1/(xy)得[1/y+2+1/x]/[2/y-3+2/x]整理得[(1/x+1/y)+2]/[2(1/x+1/y)-3]将已知

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

x-y分之xy=-3分之1xy分之(x-y)=-3x-y=-3xyx-2xy-y分之2x+3xy-2y=(-6xy+3xy)/(-3xy-2xy)=3/5

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

已知：1/X-1/Y=5通分：(Y-X)/XY=5,倒数：XY/(Y-X)=1/5.

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

(3x+5xy-3y)/(x-xy-y)=(3x-3xy-3y+8xy)/(x-xy-y)=3+8xy/(x-xy-y)=3+8/(1/y-1-1/x)=3+8/(-3)=1/3

∵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