Răspuns:
1986
Explicație pas cu pas:
[tex]2,(6) = \frac{26 - 2}{9} = \frac{8}{3} \\ [/tex]
[tex]\frac{a}{ \frac{1}{3} } = \frac{b}{3} = \frac{c}{ \frac{8}{3} } = \frac{d}{2} = k \\ 3a = \frac{b}{3} = \frac{3c}{8}= \frac{d}{2} = k[/tex]
[tex]3a = k = > a = \frac{k}{3} \\ [/tex]
[tex]\frac{b}{3} = k = > b = 3k \\ [/tex]
[tex]\frac{3c}{8} = k = > c = \frac{8k}{3} \\ [/tex]
[tex]\frac{d}{2} = k = > d = 2k \\ [/tex]
[tex]a + b + c + d = 25[/tex]
[tex]\frac{k}{3} + 3k + \frac{8k}{3} + 2k = 25 \\ k + 9k + 8k + 6k = 75 \\ 25k = 75 = > k = 3[/tex]
[tex]a = \frac{k}{3} = > a = 1 \\ [/tex]
[tex]b = 3k = > b = 9[/tex]
[tex]c = \frac{8k}{3} = > c = 8 \\ [/tex]
[tex]d = 2k = > d = 6[/tex]
[tex] = > \overline {abcd} = 1986[/tex]
