Question

\(\sqrt[3]{\left(65+x\right)^2}+4\sqrt[3]{\left(65-x\right)^2}=5\sqrt[3]{65^2-x^2}\)

Answer 1

Đặt \(\hept{\begin{cases}\sqrt[3]{65+x}=a\\\sqrt[3]{65-x}=b\end{cases}}\)

\(\Rightarrow a^2+4b^2=5ab\)

\(\Leftrightarrow\left(b-a\right)\left(4b-a\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}a=b\\a=4b\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\sqrt[3]{65+x}=\sqrt[3]{65-x}\\\sqrt[3]{65+x}=4\sqrt[3]{65-x}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}65+x=65-x\\65+x=4\left(65-x\right)\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=39\end{cases}}\)