Question

\(\overline{abbc}=\overline{ab}.\overline{ac}.7\)

Answer 1

\(\overline{abbc}=\overline{ab}.\overline{ac}.7\)

\(\Rightarrow100\overline{ab}+\overline{bc}=\overline{ab}.\overline{ac}.7\)

\(\Rightarrow100+\dfrac{\overline{bc}}{\overline{ab}}=7\overline{ac}\)

Vì \(\dfrac{\overline{bc}}{\overline{ab}}\le9\) nên \(7\overline{ac}\le109\). \(\Rightarrow9< \overline{ac}< 16\)

\(\Rightarrow\overline{ac}=10;11;12;13;14;15\)

Mà \(7\overline{ac}>100\) nên \(\overline{ac}=15\) hay a = 1; c = 5

\(\Rightarrow\dfrac{\overline{b5}}{\overline{1b}}=5\)

\(\Rightarrow10b+5=5\left(10+b\right)\)

\(\Rightarrow10b+5=50+5b\)

\(\Rightarrow5b=45\)

\(\Rightarrow b=9\)

Vậy, a = 1; b = 9; c = 5.