Toán Lớp 9: Tìm x để A=7√x−2 / 2√x+1 ngyên dương
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Toán Lớp 9: Tìm x để A=7√x−2 / 2√x+1 ngyên dương
Comments ( 1 )
Dkxd:x \ge 0\\
A > 0\\
\Leftrightarrow \dfrac{{7\sqrt x – 2}}{{2\sqrt x + 1}} > 0\\
\Leftrightarrow 7\sqrt x – 2 > 0\\
\Leftrightarrow \sqrt x > \dfrac{2}{7}\\
A = \dfrac{{7\sqrt x – 2}}{{2\sqrt x + 1}} \in N\\
\Leftrightarrow \left( {7\sqrt x – 2} \right) \vdots \left( {2\sqrt x + 1} \right)\\
\Leftrightarrow 2\left( {7\sqrt x – 2} \right) \vdots \left( {2\sqrt x + 1} \right)\\
\Leftrightarrow 14\sqrt x – 4 \vdots \left( {2\sqrt x + 1} \right)\\
\Leftrightarrow 7.\left( {2\sqrt x + 1} \right) – 11 \vdots \left( {2\sqrt x + 1} \right)\\
\Leftrightarrow 11 \vdots \left( {2\sqrt x + 1} \right)\\
\Leftrightarrow 2\sqrt x + 1 = 11\\
\Leftrightarrow 2\sqrt x = 10\\
\Leftrightarrow \sqrt x = 5\\
\Leftrightarrow x = 25\left( {tmdk} \right)\\
Vậy\,x = 25
\end{array}$