Question

HELP ME

Tìm x nguyên để các số sau có giá trị là số nguyên

a,A = 5/x+2    b,B = x-5/x    c,C =x-2/x+1    d,2x-7/x+1

Answer 1

`a)A` nguyên `<=>x+2 in Ư_5`

  Mà `Ư_5 ={+-1;+-5}`

`@x+2=1=>x=-1`

`@x+2=-1=>x=-3`

`@x+2=5=>x=3`

`@x+2=-5=>x=-7`

______________________________________________

`b)B=[x-5]/x=1-5/x`

 `B` nguyên `<=>x in Ư_{5}`

   Mà `Ư_{5}={+-1;+-5}`

 `=>x in {+-1;+-5}`

______________________________________________

`c)C=[x-2]/[x+1]=[x+1-3]/[x+1]=1-3/[x+1]`

   `C` nguyên `<=>x+1 in Ư_3`

  Mà `Ư_3={+-1;+-3}`

`@x+1=1=>x=0`

`@x+1=-1=>x=-2`

`@x+1=3=>x=2`

`@x+1=-3=>x=-4`

______________________________________________

`d)D=[2x-7]/[x+1]=[2x+2-9]/[x+1]=2-9/[x+1]`

  `D` nguyên `<=>x+1 in Ư_9`

 Mà `Ư_9 ={+-1;+-3;+-9}`

`@x+1=1=>x=0`

`@x+1=-1=>x=-2`

`@x+1=3=>x=2`

`@x+1=-3=>x=-4`

`@x+1=9=>x=8`

`@x+1=-9=>x=-10`