Question

Answer 1

\(P=\dfrac{\sqrt{x}-1}{\sqrt{x}}-9\sqrt{x}=1-\dfrac{1}{\sqrt{x}}-9\sqrt{x}=1-\left(\dfrac{1}{\sqrt{x}}+9\sqrt{x}\right)\)
Áp dụng BĐT Cô-si ta có:

\(1-\left(\dfrac{1}{\sqrt{x}}+9\sqrt{x}\right)\le1-2\sqrt{\dfrac{1}{\sqrt{x}}.9\sqrt{x}}=1-2.3=-5\)

Dấu "=" xảy ra \(\Leftrightarrow\dfrac{1}{\sqrt{x}}=9\sqrt{x}\Leftrightarrow1=9x\Leftrightarrow x=\dfrac{1}{9}\)

Vậy \(P_{max}=-5\Leftrightarrow x=\dfrac{1}{9}\)