Question

已知x+y=-9,xy=20,求y+1/x+1+x+1/y+1 的值

Answer 1

【参考答案】

简便做法：

[(y+1)/(x+1)]+[(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]
=[(-9)²-2×20+2×(-9)+2]/[20+(-9)+1]
=[81-40-16]/12
=25/12

Answer 2

因为x+y=-9,xy=20
所以x²+y²
=（x+y）²-2xy
=81-40
=41，
所以（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）
=(y²+2y+1+x²+2x+1)/(xy+x+y+1)
=（41-18+2）/(20-9+1)
=25/12

Answer 3

原式=[(x+1)^2+(y+1)^2]/(x+1)(y+1)
=[x^2+y^2+2(x+y)+2]/(xy+y+x+1)
=[(x+y)^2-2xy+2(x+y)+2]/(xy+x+y+1)
把X+Y=-4,XY=-12带入进去
得[(-4)^2+24-8+2]/(-15)
=-34/15
[若原式=(x+1)/(y+1)+(y+1)/(x+1)]
x^2为x的平方
参考资料：http://zhidao.baidu.com/question/388351602.html

追问

x+y=-9,xy=20

追答

原式=[(x+1)^2+(y+1)^2]/(x+1)(y+1)
=[x^2+y^2+2(x+y)+2]/(xy+y+x+1)
=[(x+y)^2-2xy+2(x+y)+2]/(xy+x+y+1)
把X+Y=-9,XY=20带入进去
得[(-9)^2-40-18+2]/(20-9+1)
=25/12

Answer 4

解：原式=【（y+1)²+(x+1)²]/(x+1)(y+1)=[(x+y)²-2xy+2(x+y)+2]/[xy+(x+y)+1]
=(81-40-18+2)/(20-9+1)=25/12