\(\left|a^2-3a+1\right|=1\)
\(\Leftrightarrow\left[{}\begin{matrix}a^2-3a+1=1\\a^2-3a+1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a\left(a-3\right)=0\\\left(a-2\right)\left(a-1\right)=0\end{matrix}\right.\Leftrightarrow a\in\left\{0;3;2;1\right\}\)
\(\dfrac{2a^3-12a^2+17a-a-2}{a-2}=\dfrac{2a^3-12a^2+16a-2}{a-2}\)
\(=\dfrac{2a^3-4a^2-8a^2+16a-2}{a-2}\)
\(=2a^2-8a-\dfrac{2}{a-2}\)
Khi a=2 thì A không có giá trị
Khi a=1 thì \(A=2-8-\dfrac{2}{1-2}=-6+2=-4\)
Khi a=0 thì \(A=0-0-\dfrac{2}{0-2}=-\dfrac{2}{-2}=1\)
Khi a=3 thì \(A=2\cdot9-8\cdot3-\dfrac{2}{3-2}=18-24-2=-8\)
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