Question

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } =$
plz suggest an easy method for mcqs

Answer 1

$Given : \frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} }$

$\frac{( \sqrt{2} - \sqrt{3} - \sqrt{5}) + ( \sqrt{2}+ \sqrt{3}- \sqrt{5})}{( \sqrt{2} + \sqrt{3}- \sqrt{5} )( \sqrt{2} - \sqrt{3}- \sqrt{5} ) }$

$\frac{2 \sqrt{5} - 2 \sqrt{2} }{( \sqrt{2} + \sqrt{3} - \sqrt{5} )( \sqrt{2} - \sqrt{3} - \sqrt{5}) }$

$- \frac{2 \sqrt{5} - 2 \sqrt{2} }{( \sqrt{2} + \sqrt{3} - \sqrt{5} )( \sqrt{2} - \sqrt{3} - \sqrt{5} ) }$

$- \frac{2 \sqrt{5} - 2 \sqrt{2} }{4 - 2 \sqrt{10} }$

$- \frac{2( \sqrt{5} - \sqrt{2}) }{2(2 - \sqrt{10})}$

$- \frac{ \sqrt{5} - \sqrt{2} }{2 - \sqrt{10} }$

$- \frac{ (\sqrt{5} - \sqrt{2})(2 + \sqrt{10}) }{(2 - \sqrt{10} )(2 + \sqrt{10}) }$

$-\frac{3 \sqrt{2} }{-6}$

$\frac{ \sqrt{2} }{2}$



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks