Question

Giải phương trình: \(\left(x^3-4\right)^3=\left(\sqrt[3]{\left(x^2+4\right)^2}+4\right)^2\)

 

Answer 1

Đặt \(\hept{\begin{cases}\sqrt{x^3-4}=a\\4=x^3-a^2\end{cases}}\)

\(\Rightarrow a^3=\sqrt[3]{\left(x^2+4\right)^2}+4\)

\(\Leftrightarrow x^2+a^3=x^2+\sqrt[3]{\left(x^2+4\right)^2}+4\)

\(\Leftrightarrow a^3+\sqrt[3]{\left(a^2+4\right)^2}=x^2+\sqrt[3]{\left(x^2+4\right)^2}+4\)

\(\Leftrightarrow a^3+a^2+\sqrt[3]{\left(a^2+4\right)^2}=x^3+x^2+\sqrt[3]{\left(x^2+4\right)^2}\)

\(\Leftrightarrow a=x\)

\(\Leftrightarrow x^3-4=x^2\)

\(\Leftrightarrow x=2\)