Câu hỏi của Ciel Phantomhive

Question

Tìm a,b,c biết:

$\overline{abbc}=\overline{ab}\cdot\overline{ac}\cdot7$

nguyen ngoc son · Accepted Answer

abbc=100.ab+bc

ab.ac.7-100.ab=bc

ab.(ac.7-100)=bc

$\Rightarrow\Rightarrow$ ac.7-100 < 10

$\Rightarrow\Rightarrow$ ac<16

$\Rightarrow\Rightarrow$ a=1

Ma ac.7-100=1c.7-100=c.7+70-100=c.7-30<10

$\Rightarrow\Rightarrow$ c.7<40

$\Rightarrow\Rightarrow$ c<6

va c.7-30>0

$\Rightarrow\Rightarrow$ c.7 >30

$\Rightarrow\Rightarrow$ c>4

$\Rightarrow\Rightarrow$ c=5

Ma 1c.7-100=15.7-100=5

$\Rightarrow\Rightarrow$ ab.5=bc

Hay 1b.5=b5

$\Rightarrow\Rightarrow$ 50+5b=10.b+5

$\Rightarrow\Rightarrow$ 5.b=45

$\Rightarrow\Rightarrow$ b=9

Vay a=1;b=9;c=5

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