Notez xy (barat) = n
După ce efectuăm calculele din paranteza dreaptă, ecuația devine
[tex]\it \left(\dfrac{2}{3}\right)^2 \cdot\dfrac{3}{2} +\dfrac{25}{10} =\dfrac{1}{6}n \Rightarrow \dfrac{4}{9 }\cdot\dfrac{3}{2} +\dfrac{5}{2} = \dfrac{1}{6}n \Rightarrow \dfrac{4}{6} +\dfrac{5}{2} = \dfrac{1}{6}n \Rightarrow
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\dfrac{19}{6} =\dfrac{n}{6} \Rightarrow n = 19 \Rightarrow \overline{xy} = 19[/tex]
Avem, la final, trei fracții echivalente:
[tex]\it \dfrac{12}{2t+1} =\dfrac{6z+4}{35} =\dfrac{4}{5}
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\dfrac{12}{2t+1} =\dfrac{^{3)}4}{\ 5} \Rightarrow \dfrac{12}{2t+1} = \dfrac{12}{15} \Rightarrow 2t+1 = 15 \Rightarrow 2t = 14 \Rightarrow t=7[/tex]
[tex]\it \dfrac{6z+4}{35} =\dfrac{^{7)}4}{\ 5} \Rightarrow \dfrac{6z+4}{35} =\dfrac{28}{35} \Rightarrow 6z+4 = 28 \Rightarrow 6z = 24 \Rightarrow z = 4[/tex]
Deci :
[tex]\it \overline{xyzt} = 1947[/tex]
