Question

tim gia tri nho nhat cua P=\(\frac{x+3\sqrt{x}+2}{x}\)

Answer 1

\(P=\frac{x+3\sqrt{x}+2}{x}\)

ĐKXĐ : x > 0

\(\Rightarrow P=1+\frac{3}{\sqrt{x}}+\frac{2}{x}\)

Đặt \(\frac{1}{\sqrt{x}}=t\)

\(\Leftrightarrow P=2t^2+3t+1\)

\(\Leftrightarrow P=2\left(t^2+2.t.\frac{3}{4}+\frac{9}{16}-\frac{1}{16}\right)=2\left(t+\frac{3}{4}\right)^2-\frac{1}{8}\)

\(\Leftrightarrow P=2\left(t+\frac{3}{4}\right)^2+\frac{-1}{8}\)

Có \(2\left(t+\frac{3}{4}\right)^2\ge0\)

\(\Rightarrow P\ge-\frac{1}{8}\)

Vậy MIn P = -1/8 <=> t = -3/4

Answer 2

CTV gì mà ngu vc :)) ĐKXĐ là x dương rồi mà kết quả ra âm => óc lz