Question

Tìm GTNN của bt :

P = \(\frac{x+16}{\sqrt{x}+3}\).

Answer 1

P\(=\frac{x+16}{\sqrt{x}+3}=\sqrt{x}+\frac{16}{\sqrt{x}+3}=\sqrt{x}+3+\frac{16}{\sqrt{x}+3}-3\)

ap dung cosi cho 2 so duong \(\left(\sqrt{x}+3\right)va\frac{16}{\sqrt{x}+3}taduoc\)

\(\sqrt{x}+3+\frac{16}{\sqrt{x}+3}\ge2\sqrt{\left(\sqrt{x}+3\right)\frac{16}{\sqrt{x}+3}}\)\(\ge2\sqrt{16}=8\)

\(\sqrt{x}+3+\frac{16}{\sqrt{x}+3}-3\ge8-3=5\)

dau = xay ra <=> \(\left(\sqrt{x}+3\right)=\frac{16}{\sqrt{x}+3}\)

<=>  x=1