求x=y^2,x y=2所围成的面积,并求此图形绕y轴旋转而生成的体积

由X+Y=3XY可得X+Y-XY=2XY,用X+Y-XY替换分母中的2XY,所以(2X+2Y-XY)/(X+Y+2XY)=(2X+2Y-XY)/(2X+2Y-XY)=1

x-xy=8(1)xy-y=-9(2)则有(1)-(2):X-XY-XY+Y=X+Y-2XY=8-(-9)=17

x-y=2xy3x-5xy-3y/x+xy-y=[3(x-y)-5xy]/[(x-y)+xy]=(6xy-5xy)/(2xy+xy)=1/31/x+1/y=4y+x=4xyx-5xy+y/2x+xy+

两个截距分别带入x=0得到y轴截距2y=0x1所以定义域三角形面积为1f(x,y)=1在上述给定区域fX(x)=∫(0~2-2x)1dy=2-2x0

x^2+xy+y=14y^2+xy+x=28两式相加x^2+y^2+2xy+x+y=42(x+y)^2+(x+y)-42=0(x+y-6)(x+y+7)=0x+y=6或x+y=-7

y-x-2xy=0y-x=2xyx-y=-2xy(3x+xy-3y)/(y-xy-x)=[3(x-y)+xy]/[(y-x)-xy]=(-6xy+xy)/(2xy-xy)=-5xy/xy=-5

-xy（x^2y^5-xy^3-y)=-(xy^2)^3+(xy^2)^2+xy^2=-(-2)^3+4-2=8+4-2=10

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

3x=xy+3y,xy=3x-3y2x+xy-2y/y-x-xy=(2x+3x-3y-2y)/(y-x-3x+3y)=(5x-5y)/[-(2x-2y)]=5/(-2)=-5/2

x+y=3xy,所以2x+2y-xy/x+y+2xy=(2×3xy-xy)/(3xy+2xy)=5/5=1

原式=[4(x+y)-2xy]分之[(x+y)+xy]=[4(3xy)-2xy]分之[(3xy)+xy]=10xy分之2xy=5分之1

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

因为xy/x+y=3,所以xy=3（x+y）（1）将式子（1）代入求值式子：2x-3xy+2y/-x+3xy-y=2x-9x-9y+2y/-x+9x+9y-y=-7x-7y/8x+8y=-7/8

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

3/5再问：详细过程呢再答：y-x=3xyx-y=-3xy代入得：(-6xy+3xy)/(-3xy-2xy)=-3/-5=3/5

xy/x+y=3即：xy=3(x+y)(2x-3xy+2y)/(-x+3xy-y)=[2(x+y)-3xy]/[3xy-(x+y)]=[2(x+y)-9(x+y)]/[9(x+y)-(x+y)]=-7

xy/(x+y)=2xy=2(x+y)(3x-5xy+3y)/(-x+2xy-y)=[3(x+y)-5xy]/[2xy-(x+y)]=[3(x+y)-10(x+y)]/[4(x+y)-(x+y)]=-

∵x-y/xy=3∴x-y=3xy2x+3xy-2y/x-2xy-y=[2(x-y)+3xy]/[(x-y)-2xy]=(6xy+3xy)/(3xy-2xy)=9xy/(xy)=9

x+y=5xy（2x-3xy+2y)/(x+2xy+y）=[2（x+y）-3xy]/[(x+y)+2xy]=(2×5xy-3xy)/(5xy+2xy)=7xy/7xy=1再问：若x＋1/x＝3,求(x

x-y=(x-xy)+(xy-y)=40+(-20)=20x+y-2xy=(x-xy)-(xy-y)=60