[tex]Notez~E(x)= \sqrt[3]{x-1}+ \sqrt[3]{x+1}. \\ \\ i)~Pentru~x=1,~avem:~E(1)= \sqrt[3]{2}~(deci~x=1~este~solutie) \\ \\ ii)~Pentru~x\ \textless \ 1~avem~ \sqrt[3]{x-1}\ \textless \ 0~si~ \sqrt[3]{x+1}\ \textless \ \sqrt[3]{2},~deci~in~acest \\ \\ caz~E(x)\ \textless \ \sqrt[3]{2} \Rightarrow nu ~sunt~solutii~in~intervalul~(- \infty ; 1) \\ \\ iii)~Pentru~x\ \textgreater \ 1~avem~E(x)\ \textgreater \ E(1)= \sqrt[3]{2},~deci~nici~acest~caz~nu~ \\ \\ genereaza~solutii. \\ \\ Prin~urmare,~unica~solutie~este~x=1. [/tex]
