\(Q=x^2+\frac{1}{8x}+\frac{1}{8x}+y^2+\frac{1}{8y}+\frac{1}{8y}+\frac{3}{4}\left(\frac{1}{x}+\frac{1}{y}\right)\)
\(Q\ge3\sqrt[3]{\frac{x^2}{8x.8x}}+3\sqrt[3]{\frac{y^2}{8y.8y}}+\frac{3}{4}.\frac{4}{x+y}\)
\(Q\ge\frac{3}{4}+\frac{3}{4}+\frac{3}{x+y}\ge\frac{3}{2}+\frac{3}{1}=\frac{9}{2}\)
\(Q_{min}=\frac{9}{2}\) khi \(x=y=\frac{1}{2}\)
Đề là \(Q=x^2+\frac{1}{x}+y^2+\frac{1}{y}\) hay \(\frac{x^2+1}{x}+\frac{y^2+1}{y}\) bạn?