Question

已知y=y1+y2,y1与x+1成正比例,y2与x+1成反比例,当x=0时,y=-5时;当x=2时,y=-7时.当y=-

Answer 1

由已知设y1=m(x+1),y2=n/(x+1) (m,n均为非零常数)

y=y1+y2=m(x+1)+n/(x+1)

令x=0,y=-5,得

m+n=-5 (1)

令x=2 y=-7,得

3m+n/3=-7

整理,得

9m+n=-21 (2)

(2)-(1)

8m=-16

m=-2,代入(1)

n=-5-m=-5-(-2)=-3

y=-2(x+1)-3/(x+1)=-2x -3/(x+1) -2

y=-2x代入

-2x-3/(x+1)-2=-2x

3/(x+1)=-2

x+1=-3/2

x=-5/2