Question

tìm GTNN của P, P= \(\dfrac{x+9}{6\sqrt{x}}\)

đkxđ: x ≥ 0; x ≠ 4

( áp dụng bđt cosi)

Plssssss help me🥺

Answer 1

\(ĐKXĐ:x>0\)

\(P=\dfrac{x+9}{6\sqrt{x}}=\dfrac{x-6\sqrt{x}+9+6\sqrt{x}}{6\sqrt{x}}=\dfrac{\left(\sqrt{x}-3\right)^2}{6\sqrt{x}}+1\ge1\)

Dấu "=" xảy ra \(\Leftrightarrow\sqrt{x}-3=0\Leftrightarrow x=9\)

Vậy \(MinP=1\)

Answer 2

\(P=\dfrac{x+9}{6\sqrt{x}}=\dfrac{x}{6\sqrt{x}}+\dfrac{9}{6\sqrt{x}}=\dfrac{\sqrt{x}}{6}+\dfrac{9}{6\sqrt{x}}\ge2\sqrt{\dfrac{9}{6.6}}=1\)

\(dấu"="\Leftrightarrow\dfrac{\sqrt{x}}{6}=\dfrac{9}{6\sqrt{x}}\Leftrightarrow x=9\)