已知关于xy的双曲线 求3x的平方减去4xy的最小值
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![已知关于xy的双曲线 求3x的平方减去4xy的最小值](/uploads/image/f/4243247-71-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%85%B3%E4%BA%8Exy%E7%9A%84%E5%8F%8C%E6%9B%B2%E7%BA%BF+%E6%B1%823x%E7%9A%84%E5%B9%B3%E6%96%B9%E5%87%8F%E5%8E%BB4xy%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
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-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+
=-x-(2y-2+3x)+2(x+4)=-x-2y+2-3x+2x+8=-4x-2y+10
xy/x+y=3xy=3(x+y)3x-5xy+3y/-x+3xy-y=(3x+3y)-5*3(x+y)/[-x-y+3*3(x+y)]=-12(x+y)/8(x+y)=-3/2望采纳,谢谢!
因为x/y=2所以x=2y是[x^2-xy+3y^2]/[x^2+xy+6y^2]吧=(4y^2-2y^2+3y^2)/(4y^2+2y^2+6y^2)=5y^2/12y^2=5/12
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
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
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
xy/x+y=1/2xy=2(x+y)3x-xy+3y/x-xy+y=[3(x+y)-2(x+y)]/[(x+y)-2(x+y)]=(x+y)/[-(x+y)]=-1
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
y-x-2xy=0所以x-y=-2xyy-x=2xy所以原式=[3(x-y)+xy]\[(y-x)-xy]=[3×(-2xy)+xy]\(2xy-xy)=-5xy\xy=-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=6∴xy=6(x+y)3x-2xy+3y/-x+3xy-y=[3x-12(x+y)+3y]/[-x+18(x+y)-y]=-9(x+y)/17(x+y)=-9/17再问:你在啊?再答:在
因为不知道焦点所在的坐标轴,则当焦点在x轴上时设双曲线为x^2/a^2-y^2/b^2=1由双曲线渐近线为y=正负根号3X可知,b/a=根号3则b^2/a^2=3①又焦点是(0,c)根据点到直线距离公
xy/x+y=3xy=3(x+y)3x-5xy+3y/-x+3xy-y=3x-15(x+y)+3y/-x+9(x+y)-y=-12(x+y)/8(x+y)=-3/2
3(x^2-xy)-xy+y^2=3(x^2-xy)-(xy-y^2)=3*5-(-3)=15+3=18
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