\(x=0\) không phải nghiệm của BPT
\(\left(x-1\right)\left(x-2\right)\left(x-4\right)\left(x-8\right)\le4x^2\)
\(\Leftrightarrow\left(x^2-9x+8\right)\left(x^2-6x+8\right)\le4x^2\)
\(\Leftrightarrow\frac{\left(x^2-9x+8\right)\left(x^2-6x+8\right)}{x^2}\le4\)
\(\Leftrightarrow\left(x+\frac{8}{x}-9\right)\left(x+\frac{8}{x}-6\right)-4\le0\)
\(\Leftrightarrow\left(x+\frac{8}{x}-9\right)^2+3\left(x+\frac{8}{x}-9\right)-4\le0\)
\(\Leftrightarrow\left(x+\frac{8}{x}-10\right)\left(x+\frac{8}{x}-5\right)\le0\)
\(\Leftrightarrow\left(x^2-10x+8\right)\left(x^2-5x+8\right)\le0\)
\(\Leftrightarrow x^2-10x+8\le0\)
\(\Leftrightarrow5-\sqrt{17}\le x\le5+\sqrt{17}\)
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