Question

[Hoàng Nguyễn huy]

Tìm số số x \(\in\) N thỏa mãn:

(x + 4) \(⋮\)(x+1)

Answer 1

[Trần Quỳnh Mai]

Vì : \(\frac{x+4}{x+1}\) mà \(\frac{x+1}{x+1}\Rightarrow\frac{\left(x+4\right)-\left(x+1\right)}{x+1}\Rightarrow\frac{x+4-x-1}{x+1}\Rightarrow\frac{3}{x+1}\Rightarrow x+1\inƯ\left(3\right)\)

Mà : \(Ư\left(3\right)=\left\{1;3\right\}\)

+) Nếu x + 1 = 1 => x = 1 - 1 => x = 0

+) Nếu x + 1 = 3 => x = 3 - 1 => x = 2

Vậy \(x\in\left\{0;2\right\}\) thì : \(x+4⋮x+1\)

Answer 2

[Ken Tom Trần]

\(\left(x+4\right)⋮\left(x+1\right)\Leftrightarrow\left(x+1\right)+3⋮\left(x+1\right)\)

Mà \(\left(x+1\right)⋮\left(x+1\right)\) nên để \(\left(x+4\right)⋮\left(x+1\right)\)thì \(3⋮\left(x+1\right)\)

\(\Rightarrow\left(x+1\right)\in\)U(3)

\(\Rightarrow\left(x+1\right)\in\left\{1;3;-1;-3\right\}\)

\(\Rightarrow x\in\left\{0;2;-2;-4\right\}\)

Vậy để \(\left(x+4\right)⋮\left(x+1\right)\)thì \(x\in\left(0;2;-2;-4\right)\)