\(B=\left(1-\frac{1}{x^2}\right)\left(1-\frac{1}{y^2}\right)\)
\(=\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right)\left(1-\frac{1}{x}\right)\left(1-\frac{1}{y}\right)\)
\(=\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right)\cdot\frac{x-1}{x}\cdot\frac{y-1}{y}\)
\(=\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right)\cdot\frac{\left(-x\right)\left(-y\right)}{xy}\)
\(=\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right)\)
\(=1+\frac{1}{x}+\frac{1}{y}+\frac{1}{xy}=1+\frac{x+y}{xy}+\frac{1}{xy}\)
\(=1+\frac{2}{xy}\ge1+\frac{2}{\frac{\left(x+y\right)^2}{4}}=1+\frac{2}{\frac{1}{4}}=1+8=9\)
Vậy GTNN của B = 9 khi \(x=y=\frac{1}{2}\)
