Question

please solve fast with explained ​

Answer 1

Answer:

$- (\sqrt{2} + \sqrt{5} ) - \frac{( \sqrt{110} + 4 \sqrt{11} ) }{6}$

Step-by-step explanation:

Whenever we have a rational denominator we have to rationalise the denominator with its rational factor, which is obtained by changing the negative aggregate to positive or vice versa

$given \\ \\ \frac{2}{ \sqrt{2} + \sqrt{5} - \sqrt{11} } \\ \\ here \: we \: need \: to \: rationalize \: the \: denominator \\ \\ = \frac{2}{ (\sqrt{2} + \sqrt{5} - \sqrt{11} ) } \times \frac{(\sqrt{2} + \sqrt{5} + \sqrt{11} )}{(\sqrt{2} + \sqrt{5} + \sqrt{11} )} \\ \\ = \frac{2(\sqrt{2} + \sqrt{5} + \sqrt{11} )}{ {( \sqrt{2} + \sqrt{5}) }^{2} - { \sqrt{11} }^{2} } \\ \\ = \frac{2(\sqrt{2} + \sqrt{5} + \sqrt{11} )}{7 + 2 \sqrt{10} - 11} \\ \\ = \frac{2(\sqrt{2} + \sqrt{5} + \sqrt{11} )}{2 \sqrt{10} - 8} \\ \\ = \frac{\sqrt{2} + \sqrt{5} + \sqrt{11} }{ \sqrt{10} - 4 } \\ \\ here \: again \: we \: need \: to \: rationalize \: the \: denominator \\ \\ = \frac{(\sqrt{2} + \sqrt{5} + \sqrt{11})}{( \sqrt{10} - 4)} \times \frac{( \sqrt{10} + 4 )}{( \sqrt{10} + 4)} \\ \\ = \frac{(\sqrt{2} + \sqrt{5} + \sqrt{11})( \sqrt{10} + 4)}{ { \sqrt{10} }^{2} - {4}^{2} } \\ \\ = - \frac{( \sqrt{20} + \sqrt{50} + \sqrt{110} + 4 \sqrt{2} + 4 \sqrt{5} + 4 \sqrt{11}) }{6} \\ \\ = - \frac{( \sqrt{4 \times 5} + \sqrt{25 \times 2} + \sqrt{10 \times 11} + 4 \sqrt{2} + 4 \sqrt{5} + 4 \sqrt{11} }{6} \\ \\ = - (\sqrt{2} + \sqrt{5} ) - \frac{( \sqrt{110} + 4 \sqrt{11} ) }{6}$

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Answer 2

Answer:

Please mark my answer as brainlist