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Acacia
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Asked: Tháng Mười 25, 20202020-10-25T01:50:25+00:00 2020-10-25T01:50:25+00:00In: Môn Toán

Sin x – 1 2 Sin e t Cos x + 3. Cim GTL N, GTNN

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Sin x – 1
2 Sin e t Cos x + 3.
Cim GTL N, GTNN

sin-1-2-sin-e-t-cos-3-cim-gtl-n-gtnn

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    1. Khải Quang

      Khải Quang

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      quangkhai
      2020-10-25T01:52:24+00:00Added an answer on Tháng Mười 25, 2020 at 1:52 sáng

      Đáp án:

      $\begin{array}{l}
      y = \dfrac{{\sin x – 1}}{{2\sin x + \cos x + 3}}\\
       \Rightarrow 2y\sin x + y.\cos x + 3y = \sin x – 1\\
       \Rightarrow \left( {2y – 1} \right)\sin x + y.\cos x =  – 3y – 1\\
      Dk:{\left( {2y – 1} \right)^2} + {y^2} \ge {\left( { – 3y – 1} \right)^2}\\
       \Rightarrow 5{y^2} – 4y + 1 \ge 9{y^2} + 6y + 1\\
       \Rightarrow 4{y^2} + 10y \le 0\\
       \Rightarrow 2y\left( {2y + 5} \right) \le 0\\
       \Rightarrow  – \dfrac{5}{2} \le y \le 0\\
       \Rightarrow \left\{ \begin{array}{l}
      GTNN:y =  – \dfrac{5}{2}\\
      GTLN:y = 0
      \end{array} \right.
      \end{array}$

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