Question

please write genuine answer I will mark brainly​

Answer 1

$\sf \:prove \: that : \frac{1}{3 - \sqrt{8} } - \frac{1}{ \sqrt{8} - \sqrt{7} } + \frac{1}{ \sqrt{7} - \sqrt{6} } - \frac{1}{ \sqrt{6} - \sqrt{5} } + \frac{1}{ \sqrt{5} - 2} = 5$

Solution

$\sf \:: \implies \frac{1}{3 - \sqrt{8} } - \frac{1}{ \sqrt{8} - \sqrt{7} } + \frac{1}{ \sqrt{7} - \sqrt{6} } - \frac{1}{ \sqrt{6} - \sqrt{5} } + \frac{1}{ \sqrt{5} - 2} = 5$

$\sf : \implies \: \frac{3 - \sqrt{8} }{(3 - \sqrt{8} )(3 + \sqrt{8} )} - \frac{ \sqrt{8} - \sqrt{7} }{( \sqrt{8} - \sqrt{7} )( \sqrt{8} + \sqrt{7}) } + \frac{ \sqrt{7} - \sqrt{6} }{( \sqrt{7} - \sqrt{6} )( \sqrt{7} + \sqrt{6} )} + \frac{ \sqrt{6} - \sqrt{5} }{( \sqrt{6} - \sqrt{5})( \sqrt{6} + \sqrt{5} )} + \frac{ \sqrt{5} - 2 }{( \sqrt{5} - 2)( \sqrt{5} + 2)} = 5$

$\sf : \implies \: \frac{3 - \sqrt{8} }{9 - 8} - \frac{ \sqrt{8} - \sqrt{7} }{8 - 7} + \frac{ \sqrt{7} - \sqrt{6} }{7 - 6} - \frac{ \sqrt{6} - \sqrt{5} }{6 - 5} + \frac{ \sqrt{5} - 2 }{5 - 4} = 5$

$\sf: \implies \: 3 + 2$

$\sf: \implies5$