Câu 27
[tex](x+\frac{1}{x})^2+(y+\frac{1}{y})^2\geq \frac{(x+\frac{1}{x}+y+\frac{1}{y})^2}{2}=\frac{(\frac{1}{x}+1+\frac{1}{y})^2}{2}\geq \frac{(\frac{4}{x+y}+1)}{2}=\frac{25}{2}\\"="x=y=\frac{1}{2}[/tex]
Câu 28
[tex]x^3+x^3+\frac{1}{3}\geq 3\sqrt[3]{\frac{x^6}{3}}=3x^2.\frac{1}{\sqrt[3]{3}}\\TT:y^3+y^3+\frac{1}{3}\geq 3y^2.\frac{1}{\sqrt[3]{3}}\\z^3+z^3+\frac{1}{3}\geq 3z^2.\frac{1}{\sqrt[3]{3}}\\\rightarrow 3(x^2+y^2+z^2).\frac{1}{\sqrt[3]{3}}\leq 2(x^3+y^3+z^3)+1=2+1=3\\\rightarrow x^2+y^2+z^2\leq\sqrt[3]{3}\\"=":x=y=z=\frac{1}{\sqrt[3]{3}}[/tex]