Question

tìm x thuộc Z biết:

(x^2-7x+1) chia hết cho (x-3)

 

Answer 1

\(x^2-7x+1=x^2-6x+9-x+3-11\)

\(=\left(x-3\right)^2-\left(x-3\right)-11\)

\(=\left(x-3\right)\left(x-2\right)-11\)

\(\Rightarrow x^2-7x+1⋮x-3\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)-11⋮x-3\Leftrightarrow-11⋮x-3\)

\(\Leftrightarrow x-3\inƯ\left(-11\right)=\left\{1;-1;11;-11\right\}\)

\(\Leftrightarrow x\in\left\{4;2;14;-8\right\}\)

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