ta có : abcx 17 =2000+abc
==>abc x 16 = 2000
==>abc = 2000 : 16 =125
vậy a=1;b=2;c=5
tk mik nhé
\(\text{Tìm các chữ số a,b,c biết :}\)
\(2\overline{abc}\text{ : }17=\overline{abc}\)
\(\left(2000+\overline{abc}\right)\text{ : }17=\overline{abc}\)
\(2000\text{ : }17+\overline{abc}\text{ : }17=\overline{abc}\)
\(\Rightarrow2000\text{ : }17+\overline{abc}=\overline{abc}\cdot17\)
\(\Rightarrow117\frac{11}{17}+\overline{abc}=abc\cdot17\)
\(\text{Trừ hai vế đi }1\cdot\overline{abc}\text{ ta có : }\)
\(117\frac{11}{17}=16\cdot\overline{abc}\)
\(16\cdot\overline{abc}=\frac{2000}{17}\)
\(\overline{abc}=\frac{2000}{17}\text{ : }16\)
\(\overline{abc}=\frac{2000}{272}\)
\(\overline{abc}=\frac{125}{17}\)
\(\text{Vậy : }\overline{abc}=\frac{125}{17}\)
\(\text{Ta có :}\)
\(\overline{2abc}\text{ : }17=\overline{abc}\)
\(\Rightarrow\overline{2abc}=\overline{abc}\cdot17\)
\(\Rightarrow2000+\overline{abc}=\overline{abc}\cdot17\)
\(\text{ }\Rightarrow2000=\overline{abc}\cdot16\)
\(\Rightarrow\overline{abc}\cdot16=2000\)
\(\Rightarrow abc=2000\text{ : }16\)
\(\Rightarrow\overline{abc}=125\)
\(\text{Vậy : }a=1\)
\(b=2\)
\(c=5\)
