Question

giải pt

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

Answer 1

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

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

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

\(\Leftrightarrow x-1=0\) (ngoặc phía sau luôn dương)

\(\Rightarrow x=1\)