已知x+y=-4,xy=-12,求(y+1/x+1)+(x+1/y+1)的值.)
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/31 09:07:32
已知x+y=-4,xy=-12,求(y+1/x+1)+(x+1/y+1)的值.)
x+y=-4
两边平方
x²+2xy+y²=16
所以x²+y²=40
通分
原式=(y²+2y+1+x²+2x+1)+(x+1)(y+1)
=[(x²+y²)+2(x+y)+2]/(xy+x+y+1)
=(40-8+2)/(-12-4+1)
=-34/15
由x+y=-4和xy=-12可得x和y等于2和-6(但不知谁是2谁是-6)
(y+1)/(x+1)+(x+1)/(y+1)
=[(y+1)^2+(x+1)^2]/[(x+1)(y+1)]
=(9+25)/(3*-5)
=-34/15
x+y=-4,xy=-12
∴(x+y)²=(-4)²
x²+y²+2xy=16
x²+y²=16-2xy=16-2×(-12)=40
(y+1/x+1)+(x+1/y+1)
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
=[y²+2y+1+...
全部展开
x+y=-4,xy=-12
∴(x+y)²=(-4)²
x²+y²+2xy=16
x²+y²=16-2xy=16-2×(-12)=40
(y+1/x+1)+(x+1/y+1)
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
=[y²+2y+1+x²+2x+1]/[x+y+xy+1]
=[(x²+y²+2(x+y)+2]/[(x+y)+xy+1]
=[40+2×(-4)+2]/[(-4)+(-12)+1]
=34/(-15)
=-34/15
收起
-36/15过程太麻烦
已知X+Y=3,XY=-1,求2(X-Y)^4-9(X-Y)^2+12XY
已知x*x-4xy+4y*y=0 求[2x(x+y)-y(x+y)]/(4x*x-4xy+y*y)的值?
已知x-xy =21,xy-y=-12,分别求式子x-y与x-2xy +y
已知X+Y=2XY,求4X-5XY+4Y 除以X+XY+Y 的值
已知X+Y=2XY,求4X-5XY+4Y 除以X+XY+Y 的值
已知x+y=2xy,求4x-5xy+4y/xy-x-y的值
已知x-y=4xy,求2x+3xy-2y/x-2xy-y的值
已知x-y=3xy,求5x+2xy-5y/x-4xy-y的值
已知x-y=4xy,求x-2xy-y分之2x+3xy-2y的值!
已知x/y=2,求2x(x+y)-y(x+y)/4x²-4xy+y²
已知x×x×y×y+x×x+y×y+1=4xy,求x,y的值快
已知x+y=12,xy=9,求(x+3xy+y)/(xy+xy)的值
.已知:x-y=1,xy=-2.求:(-2xy+2 x+3y)-(3xy+2y-2x)-(x+4y+xy)的值
已知x+y=6,xy=4,求x^2y+xy^2的值~
已知x+y=4,xy=2,求x+y+3xy的值
已知x的平方+y的平方-8x+6y+25=0,求(x-y+4xy/x-y)(x+y-4xy/x+y)
已知x²+y²-8x+6y+25=0,求(x-y+4xy/x-y)(x+y-4xy/x+y)
已知x、y都是正数,且xy=4y+x+5,求xy的最小值