Đặt: \(\left\{{}\begin{matrix}5x+2=a\\2x+7=b\end{matrix}\right.\Rightarrow a-b=3a-5\)
\(\Rightarrow\left(a-b\right)^3=a^3+b^3\)
\(\Rightarrow a^3+b^3-3a^2b+3ab^2=a^3+b^3\Leftrightarrow-3ab\left(a-b\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}ab=0\\a-b=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}5x+2=0\\2x+7=0\\3x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{2}{5}\\x=-\frac{7}{2}\\x=\frac{3}{5}\end{matrix}\right.\)
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