\(a^3+b^3+8=6ab\)
\(\Leftrightarrow\left(a+b\right)^3-3ab\left(a+b\right)+8-6ab=0\)
\(\Leftrightarrow\left[\left(a+b\right)^3+2^3\right]-3ab\left(a+b+2\right)=0\)
\(\Leftrightarrow\left(a+b+2\right)\left[\left(a+b\right)^2+\left(a+b\right).2+4\right]-3ab\left(a+b+2\right)=0\)
\(\Leftrightarrow\left(a+b+2\right)\left(a^2+b^2+2ab+2a+2b+4-3ab\right)=0\)
\(\Leftrightarrow\left(a+b+2\right)\left(a^2+b^2-ab+2a+2b-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a+b+2=0\\a^2+b^2-ab+2a+2b-4=0\end{matrix}\right.\)
\(\Leftrightarrow.....\)
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