Question

[Nguyễn Lý Ái Vân]

1, Tìm số nguyên x, biết

a,x+1 chia hết cho x-1

b,3x-2 chia hết cho x+2

Answer 1

[ng thi thu ha]

a,   (x - 1) + 2 chia het cho x - 1 

    vi x - 1 chia het cho x-1 

nen   2 chia het cho x - 1 

x-1 thuoc U(2)={-2;-1;1;2}

x thuoc { -1;0;2;3}

b, (3x + 6)- 8 chia het cho x + 2 

3(x+2) - 8 chia het cho x + 2 

vi 3(x+2) chia het cho x+2 

nen 8 chia het cho x + 2

x + 2 thuoc U(8)={-8;-4;-2;-1;1;2;4;8}

x thuoc { -10;-6;-4;-3;-1;0;2;6}

tich minh nha ban oi thanks

Answer 2

[Trịnh Thành Công]

a,Ta có:

\(\frac{x+1}{x-1}=\frac{x-1+2}{x-1}=\frac{x-1}{x-1}+\frac{2}{x-1}=1+\frac{2}{x-1}\)

Suy ra x-1\(\in\)Ư(2)

Ư(2)là:[1,-1,2,-2]

Ta có bảng sau:

x-1	1	-1	2	-2
x	2	0	3	-1

Vậy x=2;0;3;-1

b,Ta có:

\(\frac{3x-2}{x+2}=\frac{3x+4-6}{x+2}=\frac{3\left(x+2\right)-6}{x+2}=\frac{x+2}{x+2}-\frac{6}{x+2}=1-\frac{6}{x+2}\)

Suy ra x+2\(\in\)Ư(6)

Ư(6)là:[1,-1,2,-2,3,-3,6,-6]

Ta có bảng sau:

x+2	1	-1	2	-2	3	-3	6	-6
X	-1	-3	0	-4	1	-5	4	-8

Vậy x=-1;-3;0;-4;1;-5;4;-8