\(\left(2^x-8\right)^3+\left(4^x+13\right)^3=\left(4^x+2^x+5\right)^3\)
Đặt \(\left\{{}\begin{matrix}2^x-8=a\\4^x+13=b\end{matrix}\right.\) thì ta có:
\(a^3+b^3=\left(a+b\right)^3\)
\(\Leftrightarrow\left(a+b\right)\left(a^2-ab+b^2\right)=\left(a+b\right)^3\)
\(\Leftrightarrow ab\left(a+b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\\a+b=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2^x-8=0\\4^x+13=0\left(l\right)\\4^x+2^x+5=0\left(l\right)\end{matrix}\right.\)
\(\Rightarrow x=3\)
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