已知x2-xy-2y2＝0,且x≠0,y≠0,求代数式 的值． 公式法

由x2+xy+y2-2=0得：x2+2xy+y2-2-xy=0，即（x+y）2=2+xy≥0，所以xy≥-2；由x2+xy+y2-2=0得：x2-2xy+y2-2+3xy=0，即（x-y）2=2-3x

∵x2+5xy-6y2=0，∴（x-y）（x+6y）=0，∴x=y，x=-6y，∴（1）xy=-6或1；（2）2x−3y3x−2y=34或-1．

(x2+y2)/(x-y)=(x2+y2-2xy+2xy)/(x-y)因为xy=1,所以=[(x-y)^2+2]/(x-y)=(x-y)+2/(x-y)因为x>y>0所以(x-y)>0所以有不等式的定

x>y>0且xy＝1,则依基本不等式得：(x²+y²)/(x-y)＝[(x-y)²+2xy]/(x-y)＝(x-y)+2xy/(x-y)＝(x-y)+2/(x-y)≥2√

3x2-2xy-8y2=(3x+4y)(x-2y)=0so3x+4y=0orx-2y=0x/y=-4/3or2

∵x²-2xy-3y²=0∴*(x-3y)(x+y)=0∴x=3y或x=-y（1）2x+y/x-2y当x=3y时,原式=7y/y=7当x=-y时,原式=y/(-3y)=-1/3(2

y2＋zx＝x2=>z=(x^2-y^2)/x代入x2＋yz＝z2=>x^4+xy(x^2-y^2)=(x^2-y^2)^2=>x^4+x^3y-xy^3=x^4+y^4-2x^2y^2=>x^3-x

已知2x-3*根号(xy)-2y=0(x>0),则x2+4xy-16y2除以2x2+xy-9y2的值是多少?2x-3*根号(xy)-2y=0(根号X-2根号Y)(2根号X+根号Y)=0根号X-2根号Y

X2+Y2+8X+6Y+25=0x²+8x+16+y²+6y+9=0(x+4)²+(y+3)²=0∴x+4=0y+3=0x=-4y=-3X2+4XY+4Y2分之

A+B=2x^2－5xy－3y^2+2x^2+3xy－4y^2=4x^2-2xy-7y^2A+B－C=0C=A+B=4x^2-2xy-7y^2再问：求多项式负8x^n1－3x^n10x^n1x^n15

5

已知2x=3y,求xy／(x^2+y^2)-y^2／(x^2-y^2)的值2x=3y-->x=(3/2)yx^2=(9/4)y^2xy／(x^2+y^2)-y^2／(x^2-y^2)==(3/2)y*

x^2+y^2=3xy,因为xy不等于0,所以,两边同除以xy,得x/y+y/x=3,两边平方,得x^2y^-2+y^2x^-2=7

x²-2x+y²+6y+10=0,变换得(x-1)²+(y+3)²=0,∴x=1,y=-3∴（x2-2xy）/(xy+y2)=(1²-2*(-3))/

条件变换：(x-3)^2+(y+1)^2=0即：y+1=0x-3=0所以：立方根号x2-y2=2

2x2+5xy-3y2=0(2X-Y)(X+3Y)=0==>X=Y或者X=-3YXY不等于0,即X,Y都不等于0所以X:Y=X/Y=1或者-1/3

∵2x2+xy-3y2=0（y≠0），即（2x+3y）（x-y）=0，∴2x+3y=0，x-y=0，解得：x=-32y，x=y，当x=-32y时，xy=-32；当x=y时，xy=1．

6x2-xy-15y2=（2x+3y）（3x-5y）=0,所以x=-3/2y或x=5/3y

∵x2-y2=xy，∴原式=x2y2+y2x2=x4+y4x2y2=(x2−y2)2+2x2y2x2y2=3x2y2x2y2=3．再问：先化简2a+1/a²-1÷a²-a/a

因为x²+4y²+x²y²-6xy+1=0(x²-4xy+4y²)+(x²y²-2xy+1)=0(x-2y)²