Question

Giải phương trình: \(2+3\sqrt[3]{9x^2\left(x+2\right)}=2x+3\sqrt[3]{3x\left(x+2\right)^2}\)

Answer 1

\(2+3\sqrt[3]{9x^2\left(x+2\right)}=2x+3\sqrt[3]{3x\left(x+2\right)^2}\)

\(\Leftrightarrow2+3\sqrt[3]{3x\left(x+2\right)^2}-3\sqrt[3]{9x^2\left(x+2\right)}-2=0\)

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

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

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

\(\Leftrightarrow3x=x+2\)

\(\Leftrightarrow x=1\)

Vậy pt có một nghiệm duy nhất x = 1 ~!~"