Tìm GTNN của P=x-2căn 2x-3 ( -3 ở trong nha) Giúp mình với 24/07/2021 Bởi Bella Tìm GTNN của P=x-2căn 2x-3 ( -3 ở trong nha) Giúp mình với
Đáp án: $\begin{array}{l}P = x – 2\sqrt {2x – 3} \left( {dkxd:x \ge \dfrac{3}{2}} \right)\\ = x – 2.\sqrt 2 .\sqrt {x – \dfrac{3}{2}} \\ = x – \dfrac{3}{2} – 2.\sqrt 2 .\sqrt {x – \dfrac{3}{2}} + 2 – 2 + \dfrac{3}{2}\\ = {\left( {\sqrt {x – \dfrac{3}{2}} } \right)^2} – 2\sqrt 2 .\sqrt {x – \dfrac{3}{2}} + 2 – \dfrac{1}{2}\\ = {\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} – \dfrac{1}{2}\\Do:{\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} \ge 0\\ \Rightarrow {\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} – \dfrac{1}{2} \ge – \dfrac{1}{2}\\ \Rightarrow P \ge – \dfrac{1}{2}\\ \Rightarrow GTNN:P = – \dfrac{1}{2}\\Khi:{\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} = 0\\ \Rightarrow \sqrt {x – \dfrac{3}{2}} = \sqrt 2 \\ \Rightarrow x – \dfrac{3}{2} = 2\\ \Rightarrow x = \dfrac{7}{2}\left( {tmdk} \right)\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
P = x – 2\sqrt {2x – 3} \left( {dkxd:x \ge \dfrac{3}{2}} \right)\\
= x – 2.\sqrt 2 .\sqrt {x – \dfrac{3}{2}} \\
= x – \dfrac{3}{2} – 2.\sqrt 2 .\sqrt {x – \dfrac{3}{2}} + 2 – 2 + \dfrac{3}{2}\\
= {\left( {\sqrt {x – \dfrac{3}{2}} } \right)^2} – 2\sqrt 2 .\sqrt {x – \dfrac{3}{2}} + 2 – \dfrac{1}{2}\\
= {\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} – \dfrac{1}{2}\\
Do:{\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} \ge 0\\
\Rightarrow {\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} – \dfrac{1}{2} \ge – \dfrac{1}{2}\\
\Rightarrow P \ge – \dfrac{1}{2}\\
\Rightarrow GTNN:P = – \dfrac{1}{2}\\
Khi:{\left( {\sqrt {x – \dfrac{3}{2}} – \sqrt 2 } \right)^2} = 0\\
\Rightarrow \sqrt {x – \dfrac{3}{2}} = \sqrt 2 \\
\Rightarrow x – \dfrac{3}{2} = 2\\
\Rightarrow x = \dfrac{7}{2}\left( {tmdk} \right)
\end{array}$