Question

[(Root 5) + 2/(root 5) + 2] - [(root 5 ) + 2/(root 5) - 2]

Answer 1

$the \: value \: of \: given \: expression \: is \\ - 8 \sqrt{5} \\ \\ \color{red}{the \: given \: expression \: is} \\ \\ \frac{ \sqrt{5 - 2} }{ \sqrt{5 + 2} } = \frac{ \sqrt{5 + 2} }{ \sqrt{5 - 2} } \\ \\ \color{red}{rationlized \: the \: dinominator} \\ \\ \frac{ \sqrt{5 - 2} }{ \sqrt{5 + 2} } \times \frac{ \sqrt{5 - 2} }{ \sqrt{5 - 2} } - \frac{ \sqrt{5 + 2} }{ \sqrt{5 - 2} } \times \frac{ \sqrt{5 + 2} }{ \sqrt{5 + 2} } \\ \\ \frac{( \sqrt{5 - {2}^{2} } }{5 - 4} - \frac{( \sqrt{5 + {2}^{2} } }{5 - 4} \\ \\ 5 - 4 = \sqrt{5} - (5 + 4 \sqrt{5} ) \\ 5 - 4 = \sqrt{5} - 5 - 4 \sqrt{5} \\ - 8 \sqrt{5} \\ \\ \color{red}{therefor \: the \: value \: of \: given \: expression} \\ is \: - 8 \sqrt{5}$