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b, \(\vec{AC}+\vec{CD}-\vec{EC}\)
\(=\vec{AE}+\vec{EC}+\vec{BD}-\vec{BC}-\vec{EC}\)
\(=\vec{AE}-\vec{DB}+\vec{CB}\)
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Áp dụng BĐT cosi dạng \(\dfrac{1}{a}+\dfrac{1}{b}\ge\dfrac{4}{a+b}\)
\(\Leftrightarrow\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\cdot\dfrac{1}{4}\ge\dfrac{4}{a+b}\cdot\dfrac{1}{4}\\ \Leftrightarrow\dfrac{1}{a+b}\le\dfrac{1}{4}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\)
\(\Leftrightarrow\dfrac{a}{2a+b+c}=\dfrac{a}{a+b+a+c}\le\dfrac{a}{4}\left(\dfrac{1}{a+b}+\dfrac{1}{a+c}\right)\)
Cmtt \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{b}{a+2b+c}\le\dfrac{b}{4}\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}\right)\\\dfrac{c}{a+b+2c}\le\dfrac{c}{4}\left(\dfrac{1}{a+c}+\dfrac{1}{b+c}\right)\end{matrix}\right.\)
Cộng VTV 3 BĐT trên:
\(\Leftrightarrow VT\le\dfrac{1}{4}\left(\dfrac{a}{a+b}+\dfrac{a}{a+c}+\dfrac{b}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{a+c}+\dfrac{c}{b+c}\right)\\ \Leftrightarrow VT\le\dfrac{1}{4}\left(\dfrac{a+b}{a+b}+\dfrac{b+c}{b+c}+\dfrac{a+c}{a+c}\right)=\dfrac{1}{4}\cdot3=\dfrac{3}{4}\)
Dấu \("="\Leftrightarrow a=b=c\)
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\(\dfrac{\pi}{2}< a< \pi\Rightarrow cosa< 0\)
\(\Rightarrow cosa=-\sqrt{1-sin^2a}=-\sqrt{1-\dfrac{9}{16}}=-\dfrac{\sqrt{7}}{4}\)
\(tana=\dfrac{sina}{cosa}=-\dfrac{3\sqrt{7}}{7}\) ; \(cota=\dfrac{1}{tana}=-\dfrac{\sqrt{7}}{3}\)
Bây giờ bạn chỉ cần thay số và bấm máy tính
34D
35B
36C
37C
39B
40C
41B
42C
43B
44B
45D
46B
47D
48A
49B
50A
51C
52B
53A
54C
Thanks you so much ($-$)