Toán Lớp 7: Bài 10: Tìm số nguyên x để biểu thức nhận giá trị nguyên
c) 3-5x/2x+1
d) 2x/1-x
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Toán Lớp 7: Bài 10: Tìm số nguyên x để biểu thức nhận giá trị nguyên
c) 3-5x/2x+1
d) 2x/1-x
Comments ( 2 )
a)\dfrac{{3 – 5x}}{{2x + 1}} \in Z\\
\Leftrightarrow \left( {3 – 5x} \right) \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 2.\left( {3 – 5x} \right) \vdots \left( {2x + 1} \right)\\
\Leftrightarrow – 10x + 6 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow – 10x – 5 + 11 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow – 5.\left( {2x + 1} \right) + 11 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow 11 \vdots \left( {2x + 1} \right)\\
\Leftrightarrow \left( {2x + 1} \right) \in \left\{ { – 11; – 1;1;11} \right\}\\
\Leftrightarrow 2x \in \left\{ { – 12; – 2;0;10} \right\}\\
\Leftrightarrow x \in \left\{ { – 6; – 1;0;5} \right\}\\
Vậy\,x \in \left\{ { – 6; – 1;0;5} \right\}\\
d)\dfrac{{2x}}{{1 – x}}\\
\Leftrightarrow 2x \vdots \left( {1 – x} \right)\\
\Leftrightarrow 2x – 2 + 2 \vdots \left( {1 – x} \right)\\
\Leftrightarrow – 2.\left( {1 – x} \right) + 2 \vdots \left( {1 – x} \right)\\
\Leftrightarrow 2 \vdots \left( {1 – x} \right)\\
\Leftrightarrow \left( {1 – x} \right) \in \left\{ { – 2; – 1;1;2} \right\}\\
\Leftrightarrow x \in \left\{ {3;2;0; – 1} \right\}\\
Vậy\,x \in \left\{ {3;2;0; – 1} \right\}
\end{array}$