\(\left(x^2+8x\right)+8\left(x^2+8x\right)=48\)
Đặt: \(u=x^2+8x\)
\(\Rightarrow u^2+8u=48\)
\(\Leftrightarrow u^2+8u-48=0\)
\(\Leftrightarrow u^2-4u+12u-48=0\)
\(\Leftrightarrow u\left(u-4\right)+12\left(u-4\right)=0\)
\(\Leftrightarrow\left(u+12\right)\left(u-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}u+12=0\Leftrightarrow u=-12\\u-4=0\Leftrightarrow u=4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2+8x=-12\\x^2+8x=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+8x+12=0\\x^2+8x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-4+2\sqrt{5}\\x=-4-2\sqrt{5}\\x=-2\\x=-6\end{matrix}\right.\)
\(\Leftrightarrow x^4+16x^3+64x^2+8x^2+64x=48\\ \Leftrightarrow x^4+16x^3+72x^2+64x-48=0\\ \Leftrightarrow\left(x+2\right)\left(x+6\right)\left(x^2+8x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+6=0\\x^2+8x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-6\\x=-4\pm2\sqrt{5}\end{matrix}\right.\)
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