Toán Lớp 7: Tìm GTNN hoặc GTLN của:
D = $\frac{3/x/ + 2}{/x/ – 5}$
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Toán Lớp 7: Tìm GTNN hoặc GTLN của:
D = $\frac{3/x/ + 2}{/x/ – 5}$
Comments ( 2 )
D = \dfrac{{3\left| x \right| + 2}}{{\left| x \right| – 5}}\\
= \dfrac{{3\left| x \right| – 15 + 17}}{{\left| x \right| – 5}}\\
= \dfrac{{3\left( {\left| x \right| – 5} \right) + 17}}{{\left| x \right| – 5}}\\
= 3 + \dfrac{{17}}{{\left| x \right| – 5}}\\
Do:\left| x \right| \ge 0\\
\Leftrightarrow \left| x \right| – 5 \ge – 5\\
\Leftrightarrow \dfrac{1}{{\left| x \right| – 5}} \le – \dfrac{1}{5}\\
\Leftrightarrow \dfrac{{17}}{{\left| x \right| – 5}} \le – \dfrac{{17}}{5}\\
\Leftrightarrow 3 + \dfrac{{17}}{{\left| x \right| – 5}} \le 3 – \dfrac{{17}}{5}\\
\Leftrightarrow D \le \dfrac{{ – 2}}{5}\\
\Leftrightarrow GTLN:D = – \dfrac{2}{5}\\
Khi:x = 0
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