[tex]\Displaystyle Radicalul~fiind~de~ordin~impar,~domeniul~de~\e{de} \e{finitie}~va~fi ~\mathbb{R}. \\ \\ Avem:~\sqrt[3]{7x+1} -x=1 \Leftrightarrow \sqrt[3]{7x+1}=x+1. \\ \\ Ridicand~la~cub~ultima~relatie,~obtinem: \\ \\ 7x+1=x^3+3x^2+3x+1 \Leftrightarrow x(x^2+3x-4)=0 . \\ \\ Deci~x_1=0~sau~x^2+3x-4=0. \\ \\ x^2+3x-4=0 \Leftrightarrow (x-1)(x+4)=0 \Rightarrow x_2=1~si~x_3=-4. \\ \\ Prin~verificare~se~constata~ca~toate~aceste~solutii~sunt~bune. \\ \\ Solutie:~x \in \{-4;0;1 \}. [/tex]
[tex]\displaystyle Observatie:~In~baza~observatiei~din~primul~rand,~prin~ridicare \\ \\ la~cub~nu~exista~riscul~de~a~obtine~solutii~"in~plus"~sau~solutii \\ \\ "in~minus".~(Deci~verificarea~ramane~optionala.)[/tex]
