已知x+y=9,xy=20,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：2024/05/03 22:05:51

已知x+y=9,xy=20,求 y+1 /x+1 + x+1/ y+1 的值
已知x+y=9,xy=20,求 y+1 /x+1 + x+1/ y+1 的值

已知x+y=9,xy=20,求 y+1 /x+1 + x+1/ y+1 的值
y+1 /x+1 + x+1/ y+1
=(y+1)²/(x+1)(y+1)+(x+1)²/(x+1)(y+1)
=[(y+1)²+(x+1)²]/(x+1)(y+1)
=(x²+y²+2x+2y+2)/(xy+x+y+1)
=[(x+y)²-2xy+2(x+y)+2]/[xy+(x+y)+1]
=(81-40+18+2)/(20+9+1)
=61/30

y+1 /x+1 + x+1/ y+1
=(y+1)^2/(x+1)(y+1)+(x+1)^2/(x+1)(y+1)
=(y^2+2y+1+x^2+2x+1)/(xy+x+y+1)
=[(x^+y)^2-2xy+2(x+y)+2]/(xy+x+y+1)
=(81-40+18+2)/(20+9+1)
=61/30

x+y=9, （1）
xy=20 （2）
（1）²-（2）*4
（x-y)^2=1
x-y=1, (3)
x-y=-1 (4)
由（1）和（3）解得
x=5,y=4
y+1 /x+1 + x+1/ y+1
=5/6+6/5
=(25+36)/30
=61/30
由（1）和（4）解得

全部展开

x+y=9, （1）
xy=20 （2）
（1）²-（2）*4
（x-y)^2=1
x-y=1, (3)
x-y=-1 (4)
由（1）和（3）解得
x=5,y=4
y+1 /x+1 + x+1/ y+1
=5/6+6/5
=(25+36)/30
=61/30
由（1）和（4）解得
x=4,y=5
y+1 /x+1 + x+1/ y+1
=5/6+6/5
=(25+36)/30
=61/30
∴y+1 /x+1 + x+1/ y+1=61/30

收起

(x+y)^2=x^2+2xy+y^2=81,xy=20,x^2+y^2=81-40=41,y+1/x+1+x+1/y+1=(y^2+2y+1+x^2+2x+1)/(xy+x+y+1)=61/30

y+1 /x+1 + x+1/ y+1
=(y+1)²/(x+1)(y+1)+(x+1)²/(x+1)(y+1)
=[(y+1)²+(x+1)²]/(x+1)(y+1)
=(x²+y²+2x+2y+2)/(xy+x+y+1)
=[(x+y)²-2xy+2(x+y)+2]/[xy+(x+y)+1]
=(81-40+18+2)/(20+9+1)
=61/30
别忘了：
好的话，请采纳！！！

已知x-y=9,xy=负20,求（x+y)(x+y) 已知(1/x)-(1/y)=5,求(6x+7xy-6y)/(8y-9xy-8y) 已知,x+y=9且xy=20求1/x^2-1/y^2 已知x-xy=8,xy-y=-9,求x+y-2xy的值已知X+Y=3,XY=-1,求2(X-Y)^4-9(X-Y)^2+12XY 已知x+y=-9,xy=20,求y+1/x+1+x+1/y+1 的值已知x+y=9,xy=20,求 y+1 /x+1 + x+1/ y+1 的值已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+x(xy+y)的值已知:x-xy=40,xy-y=-20,求代数式x-y和x+y-2xy的值. 已知3/(x-y)=1/xy 求(-x-2xy+y)/ (2x+3xy-2y) 已知xy-x-y=11,求(xy-1)^2+(x+y-2)(x+y-2xy)的值. 已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+2(xy+y)的值已知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+1|+|xy+3|=0,求代数式xy^3+X^3y 已知X、Y属于R+,且XY-(X+Y)=1,求XY的范围已知x-y=9,xy=5.求(x+y)(x+y)的值?