Bài tập 84 trang 130 SGK Toán 12 NC
Bài tập 84 trang 130 SGK Toán 12 NC
So sánh p và q, biết:
\(\begin{array}{l}
a){\left( {\frac{2}{3}} \right)^p} > {\left( {\frac{3}{2}} \right)^{ - q}}\\
b){\left( {\frac{8}{3}} \right)^{ - p}} < {\left( {\frac{3}{8}} \right)^q}\\
c)0,{25^p} < {\left( {\frac{1}{2}} \right)^{2q}}\\
d){\left( {\frac{7}{2}} \right)^p} < {\left( {\frac{2}{7}} \right)^{p - 2q}}
\end{array}\)
a)
\(\begin{array}{l}
{\left( {\frac{2}{3}} \right)^p} > {\left( {\frac{3}{2}} \right)^{ - q}} \Leftrightarrow {\left( {\frac{2}{3}} \right)^p} > {\left( {\frac{2}{3}} \right)^q}\\
\Leftrightarrow p < q\,\,\left( {\frac{2}{3} < 1} \right)
\end{array}\)
b)
\(\begin{array}{l}
{\left( {\frac{8}{3}} \right)^{ - p}} < {\left( {\frac{3}{8}} \right)^q} \Leftrightarrow {\left( {\frac{3}{8}} \right)^p} < {\left( {\frac{3}{8}} \right)^q}\\
\Leftrightarrow p > q\,\,\left( {\frac{3}{8} < 1} \right)
\end{array}\)
c)
\(\begin{array}{l}
0,{25^p} < {\left( {\frac{1}{2}} \right)^{2q}} \Leftrightarrow {\left( {\frac{1}{4}} \right)^p} < {\left( {\frac{1}{4}} \right)^q}\\
\Leftrightarrow p > q\,\,\left( {\frac{1}{4} < 1} \right)
\end{array}\)
d)
\(\begin{array}{l}
{\left( {\frac{7}{2}} \right)^p} < {\left( {\frac{2}{7}} \right)^{p - 2q}} \Leftrightarrow {\left( {\frac{7}{2}} \right)^p} < {\left( {\frac{7}{2}} \right)^{2q - p}}\\
\Leftrightarrow p < 2q - p\,\,\left( {\frac{7}{2} > 1} \right)\\
\Leftrightarrow 2p < 2q \Leftrightarrow p < q
\end{array}\)
-- Mod Toán 12
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