Question

Tìm các chữ số a, b, c khác 0 thỏa mãn: abbc=ab.bc.7

la so het nhe

Answer 1

abbc=100.ab+bc

ab.ac.7-100.ab=bc

ab.(ac.7-100)=bc

\(\Rightarrow\) ac.7-100 < 10

\(\Rightarrow\) ac<16

\(\Rightarrow\) a=1

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

\(\Rightarrow\) c.7<40

\(\Rightarrow\) c<6

va c.7-30>0

\(\Rightarrow\) c.7 >30

\(\Rightarrow\) c>4

\(\Rightarrow\) c=5

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

\(\Rightarrow\) ab.5=bc

Hay 1b.5=b5

\(\Rightarrow\) 50+5b=10.b+5

\(\Rightarrow\) 5.b=45

\(\Rightarrow\) b=9

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