[TEX]y=x+\frac{11}{2x}+\sqrt{4\(1+\frac{7}{x^2}\)}[/TEX] Tìm GTNN chứ em ?
[TEX]\red note:\ \ \(1+\frac{7}{x^2}\)\(1+\frac{7}{9}\):=\(1+\frac{7}{3x}\)^2+\(\frac{\sqrt{7}}{3}-\frac{\sqrt{7}}{x}\)^2\ge \(1+\frac{7}{3x})^2[/TEX]
[TEX]\righ 4\(1+\frac{7}{x^2}\) \ge \frac{9}{4} \(1+\frac{7}{3x})^2 [/TEX]
[TEX]\righ y =x+\frac{11}{2x}+\sqrt{4\(1+\frac{7}{x^2}\)} \ge x+\frac{11}{2x}+\frac{3}{2}(1+\frac{7}{3x})[/TEX]
[TEX]\ \ \ \ =x+\frac{9}{x}+\frac{3}{2}= \(\sqrt{x}-\frac{3}{\sqrt{x}}\)^2+\frac{15}{2}\ge \frac{15}{2}[/TEX]