\(\sqrt[3]{2x+1}+\sqrt[3]{2x+2}+\sqrt[3]{2x+3}=0\)
\(\Rightarrow\left(2x+1\right)+\left(2x+2\right)+\left(2x+3\right)=3\sqrt[3]{\left(2x+1\right)\left(2x+2\right)\left(2x+3\right)}\)
\(\Leftrightarrow6x+6-3\sqrt[3]{\left(2x+1\right)\left(2x+2\right)\left(2x+3\right)}=0\)
\(\Leftrightarrow2x+2-\sqrt[3]{\left(2x+1\right)\left(2x+2\right)\left(2x+3\right)}=0\)
\(\Leftrightarrow\sqrt[3]{2x+2}\left[\sqrt[3]{\left(2x+2\right)^2}-\sqrt[3]{\left(2x+1\right)\left(2x+3\right)}\right]=0\)
Trường hợp 1:
\(\sqrt[3]{2x+2}=0\)
\(\Leftrightarrow x=-1\)
Trường hợp 2:
\(\sqrt[3]{\left(2x+2\right)^2}-\sqrt[3]{\left(2x+1\right)\left(2x+3\right)}=0\)
\(\Leftrightarrow\left(2x+2\right)^2-\left(2x+1\right)\left(2x+3\right)=0\)
\(\Leftrightarrow0x+1=0\)
Pt vô no
Vậy phương trình có 1 nghiệm duy nhất . . .