Math, asked by kalpanavinayr, 1 year ago

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

Answers

Answered by beGoodboy
2

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}

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