(x-2)y=y 2(x-2)^3求通解

再问：对不起题目打错了，是已知实数x，y满足x2+y2-2x+4y-20=0，则x2+y2的最小值是A.30-10√5B.5-5√5C.5D.25再答：更改后的答案：

x-y=1,(x-y)^2=x^2+y^2-2xy=12xy=25-1=24,xy=12(x+y)^2=x^2+y^2+2xy=25+24=49x^2-xy+y^2=25-12=13

写清楚点点比如说前面是X/X还是X/(X-Y)打上括号分段这样才能清楚的做

(x-1)^2+(y-1)^2=1令x-1=sinay-1=cosa则x=1+sina,y=1+cosax^2+y^2=1+2sina+(sina)^2+1+2cosa+(cosa)^2=3+2(si

x2+y2-6x-2y+5=0(x-3)^2+(y-1)^2=5表示一个圆,圆心坐标（3,1）x^2+y^2表示圆上一点（x,y)到原点的距离的平方.画图就看出,最大距离是：圆心到原点的距离+半径.即

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

设x+y=k,代入x2+y2+2x=0x2+(k-x)2+2x=0x2+k2-2kx+x2+2x=02x2-(2k-2)x+k2=0判别式=(2k-2)2-4*2k2>=04k2-8k+4-8k2>=

X2+Y2+8X+6Y+25=0x^2+y^2+8x+6y+25=0x^2+8x+16+y^2+6y+9=0(X+4)^2+(y+3)^2=0x=-4y=-3（x^2-4y^2)/(x^2+4xy+4

（1）x2+y2-10x-10y=0，①；x2+y2+6x-2y-40=0②；②-①得：2x+y-5=0为公共弦所在直线的方程；（2）弦心距为：|10+5−5|22+12=20，弦长的一半为50−20

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*

y^2=x^3-3x^2+2xx^2=y^3-3y^2+2y两式相减得：y^2-x^2=(x^3-y^3)-3(x^2-y^2)+2(x-y)(x-y)(x^2+xy+y^2-2x-2y+2)=0所以

[（x^2+y^2）-(x-y)^2+2y(x-y)]÷4y=1（x^2+y^2-x^2+2xy-y^2+2xy-2y^2）÷4y=1（4xy-2y^2）4y=12x-y=24x/(4x^2-y^2)

X二次方+2X+Y2次方-6Y+10=0x²+2x+1+y²-6y+9=0(x+1)²+(y-3)²=0x+1=0,y-3=0x=-1,y=3

(X+Y)²=X²+Y²+2XY=X²+Y²+X²-Y²=2X²(X-Y)²=X²+Y²-

x=0或x=整负根号下1-y方

x²-2xy+y²/x²-y²=（x-y)²/(x-y)(x+y)=（x-y)/(x+y)因为x=3,y=-5,所以（3-（-5））/（3+（-5））

x2+y2-2x+2y=6(x-1)²+(y+1)²=2²所以可设x=1+2cosay=-1+2sina于是x²+y²=(1+2cosa)²

因为x2+xy-2y2=2（x+2y）即（x-y）（x+2y）=2（x+2y）所以x-y=2（x-y）2=x2-2xy+y2=4所以xy=（x2+y2-4）/2=（20-4）/2=8（x+y）2=x2

(x-y)/(x+y)=(x-y)(x+y)/[(x+y)^2]=(x^2-y^2)/[x^2+y^2+2xy]=2xy/[x^2+y^2+x^2-y^2]=2xy/(2x^2)=y/xx^2-y^2

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