若9x=3y,且xy≠0,则我们可以除以y,-搜答案-拍题作业网

3x^2－2xy－8y^2＝0,（3x+4y)(x-2y)=03x+4y=0,或,x-2y=03x=-4y,或,x=2yx/y=-4/3,或,x/y=2

5x-6y=05x=6y所以10x=12y所以原式=(12y-4y)/(12y-3y)=8y/9y=8/9

由x+y-3xy+5=0得x+y+5=3xy．∴2xy+5≤x+y+5=3xy．∴3xy-2xy-5≥0，∴（xy+1）（3xy-5）≥0，∴xy≥53，即xy≥259，等号成立的条件是x=y．此时x

原式可变成x^2-xy+x^2-6x+9-2x+2y=x(x-y)+(x-3)^2-2(x-y)=(x-2)(x-y)+(x-3)^2=0因为x≥y≥2,所以x-2≥0,x-y≥0所以(x-2)(x-

xy≠0,所以x≠0,y≠03x²-2xy-8y²=0两边除于xy3（x/y）-2-8（y/x）=0设x/y=t;t≠03t-8/t-2=03t²-2t-8=0(t-2)

根据题意得x+y+3=0（1）x-y-2=0（2）(1)+(2)得2x+1=0∴x=-1/2把x=-1/2代入(1)得-1/2+y+3=0∴y=-5/2∴xy=5/4

xy=x^yx/y≥x^3y两式相乘,得x^2≥x^(4y)又x>1则4y≤2y≤1/2最大值为1/2点此处↓

由题设可知y=xy-1，∴x=yx3y=x4y-1，∴4y-1=1，故y=12，∴12x=x，解得x=4，于是x+y=4+12=92．故答案为：92．

若X＝3时,Y＝-4；则X－Y＝3-（-4）＝7若若X＝-3时,Y＝4；则X－Y＝-3-4＝-7

3x²+3xy=03x²=-3xy因为x不等于0所以x=-y所以x：y=1：-1

填：3x+2y-2xy=02y+3x=2xy(2y+3x)/(2xy)=1(1/x)+(3/y)=1根据均值不等式得1≥2√(3/(xy))1≥12/(xy)xy≥12所以xy的最小值是12

1x=4y代入

2分之1或负4分之3

1.若x分之1-y分之1=2,则求x-xy-y分之3x+xy-3y=0的值.若x分之1-y分之1=2变形（y-x）/xy=2,(y-x)=2xy(3x+xy-3y)/(x-xy-y)=[3(x-y)+

-2x+6xy-2y/(7x+5y)-9xy-(3x+y)=[3(x+y)-x-y]/[7x+5y-9/2(x+y)-3x-y]=2(x+y)/[-1/2(x+y)]=-4

2x+3y=8=>x=(8-3y)/2xy=(8-3y)/2*y=1/2*(-3y^2+8y)=-3/2*(y^2-8/3y+16/9)+8/3=-3/2(y-4/3)^2+3/8《8/3所以最大值为

因为,x-y=3xy所以：-3x+6xy+3y/[(7x-5y)-9xy-(3x-y)]=[-3(x-y)+6xy]/[(7x-5y)-9xy-(3x-y)]=[-3*3xy+6xy]/[7x-5y-

2X^2+3xy-2y^2=0(2x-y)(x+2y)=0即：2x-y=0或,x+2y=0y=2x或x=-2y当y=2x时：x+y/x-y=3x/(-x)=-3当x=-2y时：x+y/x-y=-y/(

∵x-y=4xy∴原式=[2(x-y)+3xy]/[-(x-y)-2xy]=(8xy+3xy)/(-4xy-2xy)=11xy/(-6xy)=-11/6