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Question

Chứng minh rằng:

a.$\overline{abcabc}$$⋮7$

b. $\overline{aaa}$ $⋮37$

c. $\overline{1ab1}$ $-\overline{1ba1}$ $⋮90$

Mashiro Shiina · Accepted Answer

Ta có:

$\overline{abcabc}=1001\overline{abc}$

$=143.7.\overline{abc}$

$\Rightarrow1001\overline{abc}⋮7\Rightarrow\overline{abcabc}⋮7$

$\rightarrowđpcm$

$\overline{aaa}=111a$

$=37.3.a$

$\Rightarrow111a⋮37\Rightarrow\overline{aaa}⋮37$

$\rightarrowđpcm$

$\overline{1ab1}-\overline{1ba1}$

$=1000+\overline{ab}+1-1000-\overline{ba}-1$

$=\overline{ab}-\overline{ba}$

$=10a+b-10b-a$

$=9a-9b$

$=9\left(a-b\right)⋮9$

Mà $\overline{1ab1}-\overline{1ba1}=\overline{...0}⋮10$

$\Rightarrow\overline{1ab1}-\overline{1ba1}⋮9;10\Rightarrow⋮90$

$\rightarrowđpcm$Câu trả lời: Ta có:

$\overline{abcabc}=1001\overline{abc}$

$=143.7.\overline{abc}$

$\Rightarrow1001\overline{abc}⋮7\Rightarrow\overline{abcabc}⋮7$

$\rightarrowđpcm$

$\overline{aaa}=111a$

$=37.3.a$

$\Rightarrow111a⋮37\Rightarrow\overline{aaa}⋮37$

$\rightarrowđpcm$

$\overline{1ab1}-\overline{1ba1}$

$=1000+\overline{ab}+1-1000-\overline{ba}-1$

$=\overline{ab}-\overline{ba}$

$=10a+b-10b-a$

$=9a-9b$

$=9\left(a-b\right)⋮9$

Mà $\overline{1ab1}-\overline{1ba1}=\overline{...0}⋮10$

$\Rightarrow\overline{1ab1}-\overline{1ba1}⋮9;10\Rightarrow⋮90$

$\rightarrowđpcm$

Chu Phương Uyên · Answer

b, ta có $\overline{aaa}$=111.a=37.3.a $⋮$37

=> aaa chia hết 37 (đpcm)Câu trả lời: b, ta có $\overline{aaa}$=111.a=37.3.a $⋮$37

=> aaa chia hết 37 (đpcm)

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