Question

Giải phương trình:

\(\sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0\)\(=0\)

Answer 1

\(\sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0\)

\(\Leftrightarrow\left(\sqrt[3]{x+1}+1\right)+\sqrt[3]{x+2}+\left(\sqrt[3]{x+3}-1\right)=0\)

\(\Leftrightarrow\frac{x+2}{\sqrt[3]{\left(x+1\right)^2}-\sqrt[3]{x+1}+1}+\frac{x+2}{\sqrt[3]{\left(x+2\right)^4}}+\frac{x+2}{\sqrt[3]{\left(x+3\right)^2}+\sqrt[3]{x+3}+1}\)(liên hợp tử mẫu)

\(\Leftrightarrow\left(x+2\right)\left(\frac{1}{\sqrt[3]{\left(x+1\right)^2}-\sqrt[3]{x+1}+1}+\frac{1}{\sqrt[3]{\left(x+2\right)^4}}+\frac{1}{\sqrt[3]{\left(x+3\right)^2}+\sqrt[3]{x+3}+1}\right)=0\)

\(\Leftrightarrow x+2=0\)( vì biểu thức thứ 2 luôn khác 0)

\(\Leftrightarrow x=-2\)

Vậy...

Answer 2

\(\left(\sqrt[3]{x+1}+\sqrt[3]{x+3}\right)\left(LH\right)=\sqrt[3]{x+2}\left(LH\right)\)

\(\Leftrightarrow2\left(x+2\right)=\sqrt[3]{x+2}\left(Lh\right)\)

=> x=-2 la nghiệm

x khác -2

\(2\sqrt[3]{\left(x+2\right)^2}=-\left(LH\right)\) Vô nghiệm