Toán Lớp 8: tìm min max nếu có : A = ((căn x) + 5 ))/ ((căn x) + 2))
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Toán Lớp 8: tìm min max nếu có : A = ((căn x) + 5 ))/ ((căn x) + 2))
Comments ( 1 )
Dkxd:x \ge 0\\
A = \dfrac{{\sqrt x + 5}}{{\sqrt x + 2}} = \dfrac{{\sqrt x + 2 + 3}}{{\sqrt x + 2}}\\
= 1 + \dfrac{3}{{\sqrt x + 2}}\\
Do:\sqrt x + 2 \ge 2\\
\Leftrightarrow \dfrac{1}{{\sqrt x + 2}} \le \dfrac{1}{2}\\
\Leftrightarrow \dfrac{3}{{\sqrt x + 2}} \le \dfrac{3}{2}\\
\Leftrightarrow 1 + \dfrac{3}{{\sqrt x + 2}} \le 1 + \dfrac{3}{2}\\
\Leftrightarrow A \le \dfrac{5}{2}\\
\Leftrightarrow GTLN:A = \dfrac{5}{2}\,khi:x = 0
\end{array}$