Question

\(\sqrt[3]{x+7}-\sqrt[3]{x-1}=2\)

Answer 1

\(\Leftrightarrow\sqrt[3]{x+7}-2-\sqrt[3]{x-1}=0\)

=>\(\dfrac{x+7-8}{\sqrt[3]{\left(x+7\right)^2}+2\sqrt[3]{x+7}+4}-\sqrt[3]{x-1}=0\)

=>\(\dfrac{x-1}{\sqrt[3]{\left(x+7\right)^2}+2\sqrt[3]{x+7}+4}-\sqrt[3]{x-1}=0\)

=>\(\sqrt[3]{x-1}\left(\dfrac{\left(\sqrt[3]{x-1}\right)^2}{\sqrt[3]{\left(x+7\right)^2}+2\sqrt[3]{x+7}+4}-1\right)=0\)

=>x-1=0

=>x=1

Answer 2