Question

[Nguyễn thị Minh Hậu]

Tìm số tự nhiên x,biết:

a,21 thuộc B(x-3)

b,1-x thuộc Ư(17)

c,2x + 3 thuộc B (2x - 1)

d,x + 1 thuộc (x²+x+3)

e,3x + 1 chia hết cho 11 - 2x

Answer 1

[Lung Thị Linh]

a, \(21\in B\left(x-3\right)\Leftrightarrow x-3\inƯ\left(21\right)\Leftrightarrow x-3\in\left\{1;3;7;21;-1;-3;-7;-21\right\}\)

\(\Leftrightarrow x\in\left\{4;6;10;24;2;0;-4;-18\right\}\)

Vì \(x\in N\Rightarrow x\in\left\{4;6;10;24;2;0\right\}\)

b, \(1-x\inƯ\left(17\right)\Leftrightarrow1-x\in\left\{1;17;-1;-17\right\}\)

\(\Leftrightarrow x\in\left\{0;-16;2;18\right\}\)

Vì \(x\in N\Rightarrow x\in\left\{0;2;18\right\}\)

c, \(2x+3\in B\left(2x-1\right)\)

\(\Leftrightarrow2x+3⋮2x-1\Leftrightarrow2x-1+4⋮2x-1\Leftrightarrow4⋮2x-1\)

\(\Leftrightarrow2x-1\inƯ\left(4\right)\Leftrightarrow2x-1\in\left\{1;2;4;-1;-2;-4\right\}\)

\(\Leftrightarrow x\in\left\{1;\frac{3}{2};\frac{5}{2};0;\frac{-1}{2};\frac{-3}{2}\right\}\)

Vì \(x\in N\Rightarrow x\in\left\{1;0\right\}\)

d, \(x+1\inƯ\left(x^2+x+3\right)\Leftrightarrow x^2+x+3⋮x+1\Leftrightarrow x\left(x+1\right)+3⋮x+1\Leftrightarrow3⋮x+1\)

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

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

Vì \(x\in N\Rightarrow x\in\left\{0;2\right\}\)