Gọi số đó là abcdef ( đk : \(a;b;c;d;e;f\in N,0< a;e< 10,0\le b;c;d;f< 10\))
Ta có:
\(\overline{efabcd}=\frac{3}{4}\overline{abcdef}\Leftrightarrow\overline{ef}.10000+\overline{abcd}=\overline{abcd}.75+\frac{3}{4}\overline{ef}\)
\(\Leftrightarrow9999\frac{1}{4}\overline{ef}=74\overline{abcd}\)
\(\Leftrightarrow135,125.\overline{ef}=\overline{abcd}\)
Ta thấy: \(1000\le\overline{abcd}\le9999\Rightarrow7< \overline{ef}< 74\)
\(135,125=135\frac{1}{8}\)mà \(\overline{abcd}\in N\Rightarrow\overline{ef⋮}8\)
\(\Rightarrow\overline{ef}\in\left\{16;24;32;40;48;56;64;72\right\}\)
Thử chọn ta tìm ra.
