Question

Tìm GTNN:

P = \(x\) - \(\sqrt{x}\)

Answer 1

ĐKXĐ : \(x\ge0\)

Có : \(P=x-\sqrt{x}=\left(\sqrt{x}\right)^2-2.\sqrt{x}.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}\)

\(=\left(\sqrt{x}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

Dấu "=" xảy ra \(\Leftrightarrow\sqrt{x}-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{4}\) ( Thỏa mãn )

Vậy Min \(P=\dfrac{1}{4}\) khi \(x=\dfrac{1}{4}\)