Toán Lớp 7: Tìm x biết x là số nguyên
B= [5x+1]/[2x+1]
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Toán Lớp 7: Tìm x biết x là số nguyên
B= [5x+1]/[2x+1]
Comments ( 1 )
B = \dfrac{{5x + 1}}{{2x + 1}} \in Z\\
\Leftrightarrow \left( {5x + 1} \right) \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 2.\left( {5x + 1} \right) \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 10x + 2 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 5.\left( {2x + 1} \right) – 3 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 3 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow \left( {2x + 1} \right) \in \left\{ { – 3; – 1;1;3} \right\}\\
\Leftrightarrow 2x \in \left\{ { – 4; – 2;0;2} \right\}\\
\Leftrightarrow x \in \left\{ { – 2; – 1;0;1} \right\}\\
\Leftrightarrow B \in \left\{ {3;4;1;2} \right\}\left( {tmdk} \right)\\
Vậy\,x \in \left\{ { – 2; – 1;0;1} \right\}
\end{array}$