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\(A=-2\left(x^2-\dfrac{1}{2}x\right)=-2\left(x^2-2.x.\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{1}{16}\right)\)
\(=-2\left(x^2-2x.\dfrac{1}{4}+\dfrac{1}{16}\right)+\dfrac{1}{8}=-2\left(x-\dfrac{1}{4}\right)^2+\dfrac{1}{8}\le\dfrac{1}{8}\)
\(\Rightarrow A_{max}=\dfrac{1}{8}\)
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Câu 1:
\(\left(4x+3\right)\left(3x^2+x-2\right)\left(2x^2-3x-5\right)=0\\ \Leftrightarrow\left(4x+3\right)\left(3x-2\right)\left(x+1\right)\left(2x-5\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=-1\\x=\dfrac{2}{3}\\x=\dfrac{5}{2}\end{matrix}\right.\\ \Leftrightarrow A=\left\{-1;-\dfrac{3}{4};\dfrac{2}{3};\dfrac{5}{2}\right\}\)
Câu 2:
\(\left(x^2-4\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=3\end{matrix}\right.\Leftrightarrow A=\left\{-2;2;3\right\}\\ \left|5x\right|-11\le0\Leftrightarrow\left|5x\right|\le11\Leftrightarrow-11\le5x\le11\\ \Leftrightarrow-\dfrac{11}{5}\le x\le\dfrac{11}{5}\\ \Leftrightarrow B=\left[-\dfrac{11}{5};\dfrac{11}{5}\right]\)
\(\Leftrightarrow A\cap B=\left\{-2;2\right\}\\ A\cup B=\left[-\dfrac{11}{5};3\right]\\ A\B=\left\{3\right\}\)
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1 am going to send
2 will get
3 will do
4 will be
5 are going to visit
6 will win
7 am going to take
8 are going
9 will go
10 is going to defeat
11 is going to have
12 will never lie
13 will fly
14 won't tell
15 will like
\(\left(\sqrt{1999}+\sqrt{2021}\right)^2\)
\(1999+2001+2\sqrt{1999.2001}\)
\(4000+2\sqrt{\left(2000-1\right)\left(2000+1\right)}\)
\(4000+2\sqrt{2000^2-1}\)
\(\left(2\sqrt{2000}\right)^2=4.2000=8000\)
\(4000+2\sqrt{2000^2}\)
\(\left(\sqrt{1999}+\sqrt{2001}\right)^2< \left(2\sqrt{2000}\right)^2\)
\(\sqrt{1999}+\sqrt{2001}< 2\sqrt{2000}\)
dòng đàu mình ghi nhầm thành\(\sqrt{2021}\)bạn sửa nha