Question

[Quân]

chứng minh rằng nếu ab+cd+eg chia hết cho 11 thì abcdeg chia hết cho 11

lm giúp mik nha

iu mn nhìu ♥♥♥

Answer 1

[Hacker♪]

Ta có:

$\overline{abcdeg}=10000\overline{ab}+\overline{100}cd+\overline{eg}$

$=9999\overline{ab}+99\overline{cd}+\overline{ab}+\overline{cd}+\overline{eg}$

$=\left(9999\overline{ab}+99\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)$

$=\left(\mathrm{11.909.}\overline{ab}+11.9\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)$

$=11\left(\mathrm{909.9.}\overline{ab}.\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)$

Mà: $\{\begin{array}{c}11\left(\mathrm{909.9.}\overline{ab}.\overline{cd}\right)⋮11\\ \left(\overline{ab}+\overline{cd}+\overline{eg}\right)⋮11\end{array}$

$\Rightarrow 11\left(\mathrm{909.9.}\overline{ab}.\overline{cd}\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)⋮11$

Hay $\overline{abcdeg}⋮11$ (Đpcm)

Answer 2

[Quân]

thanks bn nha

mà hơi dài 1 chút hihi