`a)``x^2+5vdotsx+1`

`=>x^2-1+6vdotsx+1`

`=>(x-1)(x+1)+6vdotsx+1`

Vì `(x-1)(x+1)vdotsx+1AAx in ZZ`

`=>6vdotsx+1`

Vì `x in ZZ`

`=>x+1 in Ư(6)={+-1;+-2;+-3;+-6}`

`=>x+1 in {-6;-3;-2;-1;1;2;3;6}`

`=>x in {-7;-4;-3;-2;0;1;2;5}`

Vậy `x in {-7;-4;-3;-2;0;1;2;5}`

`b)``x^2+4x-8vdotsx+3`

`=>x^2+3x+x+3-11vdotsx+3`

`=>(x^2+3x)+(x+3)-11vdotsx+3`

`=>x(x+3)+(x+3)-11vdotsx+3`

`=>(x+1)(x+3)-11vdotsx+3`

Vì `(x+1)(x+3)vdotsx+3AAx in ZZ`

`=>11vdotsx+3`

`=>x+3 in Ư(11)={+-1;+-11}`

`=>x+3 in {-11;-1;1;11}`

`=>x in {-14;-4;-2;8}`

Vậy `x in {-14;-4;-2;8}`

`c)``x+2vdots2x^2+5`

`=>(x+2)(2x-4)vdots2x^2+5`

`=>2(x+2)(x-2)vdots2x^2+5`

`=>2(x^2-4)vdots2x^2+5`

`=>2x^2-8vdots2x^2+5`

`=>2x^2+5-13vdots2x^2+5`

Vì `2x^2+5vdots2x^2+5AAx in ZZ`

`=>13vdots2x^2+5`

Vì `x in ZZ`

`=>2x^2+5 in Ư(13)={+-1;+-13}`

`=>2x^2+5 in {-13;-1;1;13}`

`=>2x^2 in {-18;-6;-4;8}`

`=>x^2 in {-9;-3;-2;4}`

Vì `x^2>=0AAx in ZZ`

`=>x^2=4`

`=>x^2=(+-2)^2`

`=>x in {-2;2}`

`=>(x+2)/(2x^2+5) in {0;4/13}`

`=>x=-2`

Vậy `x=-2`

`d)``2x^2+5vdotsx+2`

`=>2x^2+4x-4x-8+13vdotsx+2`

`=>(2x^2+4x)-(4x+8)+13vdotsx+2`

`=>2x(x+2)-4(x+2)+13vdotsx+2`

`=>(2x-4)(x+2)+13vdotsx+2`

Vì `(2x-4)(x+2)vdotsx+2AAx in ZZ`

`=>13vdotsx+2`

Vì `x in ZZ`

`=>x+2 in Ư(13)={+-1;+-13}`

`=>x+2 in {-13;-1;1;13}`

`=>x in {-15;-3;-1;11}`

Vậy `x in {-15;-3;-1;11}`