\[\boxed{\text{1048\ (1048).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x^{2} - 3,75x + a^{3} = 0,\ \ a - ?\]
\[По\ теореме\ Виета:\ \]
\[x_{1} + x_{2} = 3,75,\]
\[x_{1} \cdot x_{2} = a³.\]
\[x_{1}x_{2} = x_{2}^{2}x_{2} = x_{2}^{3} = a^{3},\]
\[x_{2} = a,\ \ x_{1} = a^{2}.\]
\[a^{2} + a = 3,75\]
\[a^{2} + a - 3,75 = 0\]
\[D = 1 + 15 = 16\]
\[a_{1} = \frac{- 1 + 4}{2} = 1,5,\ \ \]
\[a_{2} = \frac{- 1 - 4}{2} = - 2,5.\]
\[Ответ:a_{1} = 1,5;\ \ \ a_{2} = - 2,5.\]