[tex]\displaystyle\\
x+ \sqrt[3]{x} +2 =0\\\\
\texttt{Notatie:} ~~x=y^3\\\\
y^3+ \sqrt[3]{y^3}+2=0\\\\
y^3+y+2=0\\\\
\text{Observam ca }~y=-1~\text{ este solutie a ecuatiei.}\\\\
\text{Rezulta ca il putem scoate factorul: }~(y+1)\\\\
y^3+y+2=0\\\\
y^3+\underbrace{y^2-y^2-y+y} +y+2 =0\\\\
y^3+y^2-y^2-y+2y+2 =0\\\\
y^2(y+1)-y(y+1) + 2(y+1)=0\\\\
(y+1)(y^2-y+2)=0\\ \\
y-1=0~~~\Longrightarrow~~y_1=-1 \\\\
y^2-y+2)=0~~\Delta=1-8=-7\ \textless \ 0~~\Longrightarrow~~y\notin R[/tex]
[tex]\Longrightarrow~~~\texttt{ Solutie unica: }~\boxed{y = -1} \\ \\
\text{Revenim la x, necunoscuta initiala.}\\\\
\bold{x = y^3 = (-1)^3 = \boxed{\boxed{\bold{-1}}}}
[/tex]
