[tex] \left\{\begin{array}{c} \sqrt[\b3]{x} +\sqrt[\b3]{y} = 4\\\\x+y = 28~~~~\end{array}\right\\\\\\
28\in N~\Longrightarrow~x\in N~si~y\in N\\
4\in N~\Longrightarrow~\sqrt[\b3]{x} \in N~si~\sqrt[\b3]{y}\in N\\\\
\Longrightarrow~~\text{x si y sunt cuburi perfecte.}\\
\Longrightarrow~~\text{28 se poate descompune in suma de 2 cuburi perfecte.}\\\\
28=1+27=1^3+3^3\\\\
Solutia~1:\\
x=1\\
y=27\\\\
Solutia~2:\\
x=27\\
y=1\\\\
\texttt{Verificare:}\\\\
1+27=28\\\\
\sqrt[\b3]{1}+ \sqrt[\b3]{27}=1+3=4 [/tex]
