Question

tìm các số nguyên x, y sao cho:

a, 3x - 7 chia hết cho x - 3

b,4x +3 chia hết cho 2x- 1

c,x^2 + 2x - 5 chia hết cho x + 3

Answer 1

a) 3x-7 \(⋮\) x-3

\(\Leftrightarrow\) 3x-9+2 \(⋮\) x-3

\(\Leftrightarrow\) 3(x-3)+2 \(⋮\) x-3

Vì 3(x-3) \(⋮\) x-3 nên 2 \(⋮\) x-3

\(\Rightarrow\) x-3 \(\inƯ\left(2\right)=\left\{1;2;-1;-2\right\}\)

\(\Rightarrow x\in\left\{4;5;2;1\right\}\)

Vậy..........................

c) x²+2x-5 \(⋮\) x+3

\(\Leftrightarrow\) x.x+3x-x-3-2 \(⋮\) x+3

\(\Leftrightarrow\) x(x+3)-(x+3)-8 \(⋮\) x+3

Vì x(x+3)-(x+3) \(⋮\) x+3 nên 8 \(⋮\) x+3

\(\Rightarrow\) x+3 \(\inƯ\left(8\right)=\left\{1;2;4;8;-1;-2;-4;-8\right\}\)

\(\Rightarrow x\in\left\{-2;-1;1;5;-4;-5;-7;-11\right\}\)

Vậy.........................

(Câu b tương tự)

Answer 2

a) 3x - 7 chia hết cho x - 3

⇒ \(\left[{}\begin{matrix}\text{3x - 7 ⋮ x - 3}\\\text{x - 3 ⋮ x - 3}\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}\text{3x - 7 ⋮ x - 3}\\\text{3(x - 3) ⋮ x - 3}\end{matrix}\right.\)

3x - 7 chia hết cho 3(x - 3)

Do đó ta có 3x - 7 = 3(x - 3) + 2

Nên 2 ⋮ x - 3

Vậy x - 3 ∈ Ư(2) = {-1; 1; -2; 2}

Ta có bảng sau :

x - 3	-1	1	-2	2
x	2	4	1	5

➤ Vậy x ∈ {2; 4; 1; 5}

b) 4x + 3 chia hết cho 2x - 1

⇒ \(\left[{}\begin{matrix}\text{4x + 3 ⋮ 2x - 1}\\\text{2x - 1 ⋮ 2x - 1}\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}\text{4x + 3 ⋮ 2x - 1}\\\text{2(2x - 1) ⋮ 2x - 1}\end{matrix}\right.\)

4x + 3 chia hết cho 2(2x - 1)

Do đó ta có 4x + 3 = 2(2x - 1) + 5

Nên 5 ⋮ 2x - 1

Vậy 2x - 1 ∈ Ư(5) = {-1; 1; -5; 5}

Ta có bảng sau :

2x - 1	-1	1	-5	5
2x	0	2	-4	6
x	0	1	-2	3

➤ Vậy x ∈ {0; 1; -2; 3}