Question

Tìm số tự nhiên x,biết:

a,6 chia hết (2x-1)

b,x+5 chia hết(x-1)

Answer 1

a) Ta có:

\(6⋮2x-1\)

\(\Rightarrow2x-1\in U\left(6\right)=\left\{1;2;3;6\right\}\) \(\left(\text{ vì }x\in N\right)\)

\(\Rightarrow\left\{{}\begin{matrix}2x-1=1\Rightarrow x=1\\2x-1=2\Rightarrow x=1,5\left(loai\right)\\2x-1=3\Rightarrow x=2\\2x-1=6\Rightarrow3,5\left(loai\right)\end{matrix}\right.\)

Vậy x=1 hoặc x=2

b) Ta có:

\(x+5⋮x-1\)

\(\Rightarrow\left(x-1\right)+6⋮x-1\)

\(\Rightarrow6⋮x-1\)

\(\Rightarrow x-1\in U\left(6\right)=\left\{1;2;3;6\right\}\) \(\left(\text{ vì }x\in N\right)\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=1\Rightarrow x=2\\x-1=2\Rightarrow x=3\\x-1=3\Rightarrow x=4\\x-1=6\Rightarrow x=7\end{matrix}\right.\)

Vậy x=2 hoặc x=3 hoặc x=4 hoặc x=7

Answer 2

a) vì 6⋮(2x-1)

=>2x-1∈Ư(6)={1;2;3;6}

ta có bảng sau

2x-1	1	2	3	6
x	1	\(\dfrac{3}{2}\)	2	3,5
	✔	✖	✔	✖

vậy x∈{1;2}

Answer 3

b) vì x+5⋮x-1

x-1⋮x-1

=>(x+5)-(x-1)⋮x-1

=>x+5-x+1⋮x-1

=>6⋮x-1

=>x-1∈Ư(6)={1;2;3;6}

ta có bảng sau

x-1	1	2	3	6
x	2	3	4	7
	✔	✔	✔	✔

vậy x∈{2;3;4;7}