Question

Tìm các chữ số a ,b ,c biết :

abc - ac = 2cb + bc

Answer 1

a=3

b=6

c=4

Answer 2

a=3

b=6

c=4

Answer 3

\(\overline{abc}-\overline{ac}=\overline{2cb}+\overline{bc}\)

\(\Rightarrow100a+10b+c-10a-c=200+10c+b+10b+c\)

\(\Rightarrow90a+10b=200+11b+11c\)

\(\Rightarrow90a-200=11c+b\)

Vì \(90a-200>0\Rightarrow90a>200\Rightarrow a>2\)

Ta lại có: \(90a-200=11c+b\Rightarrow11c+b+200=90a\)

\(\Rightarrow11c+b:90\)dư 70

\(\Rightarrow11c+b=90k+70\)

\(\Rightarrow k=0\Rightarrow11c+b=70\)

\(\Rightarrow c=6;b=4\)

\(\Rightarrow70+200=90a\)

\(\Rightarrow90a=270\Rightarrow a=3\Rightarrow\overline{abc}=346\)