Question

1.Tìm các số tự nhiên \(x\) , sao cho :

a) (\(x\) + 19) \(⋮\) (\(x\) + 1)

b) (\(^{x^2}\) + \(3x\) + 2) \(⋮\) (\(x\) - 1)

Answer 1

a

xét x +19-(x+1)=18

để x+19 chia hết cho x+1 thì 18 chia hết cho x+1

suy ra x+1 thuộc ư(18)={1;2;3;6;9;18}

x+1=1thì x =0

x+1=2 thì x=1

x+1=3thì x=2

x+1=6thì x =5

x+1=9 thì x=8

x+1=18thì x=17

xậy ......................

Answer 2

a) ($x$ + 19) $⋮$ ($x$ + 1)

=> \(\left(x+19\right)-\left(x+1\right)⋮\left(x+1\right)\)

=> \(\left(x+19-x-1\right)⋮\left(x+1\right)\)

=> \(18⋮\left(x-1\right)\)

=> \(\left(n+1\right)\inƯ\left(18\right)=\left\{1;2;3;6;9;18\right\}\)

ta có bảng sau

n+1	1	2	3	6	9	18
n	0	1	2	5	8	17

vậy x\(\in\left\{0;1;2;5;8;17\right\}\)