Correct option is (B) √7
\(x=2\sqrt2+\sqrt7\)
\(\therefore\frac1x=\frac1{2\sqrt2+\sqrt7}=\frac{2\sqrt2-\sqrt7}{(2\sqrt2+\sqrt7)(2\sqrt2-\sqrt7)}\) \(=\frac{2\sqrt2-\sqrt7}{(2\sqrt2)^2-(\sqrt7)^2}\)
\(\Rightarrow\) \(\frac1x=\frac{2\sqrt2-\sqrt7}{8-7}=2\sqrt2-\sqrt7\)
\(\therefore x-\frac1x=(2\sqrt2+\sqrt7)-(2\sqrt2-\sqrt7)=2\sqrt7\)
\(\therefore\) \(\frac{1}{2}(x-\frac{1}{x})\) \(=\frac{2\sqrt7}2=\sqrt7\)
