Question

Sa se rezolve sistemul de ecuatie:

Answer 1

   
[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]