Question

please solve the question

Answer 1

$\large \tt AHOY!! \:$

$\sf given : - \frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } \sf \small \\ \\ \sf \small = \frac{(4 + \sqrt{5})(4 + \sqrt{5} )}{(4 - \sqrt{5} )(4 + \sqrt{5}) } + \frac{(4 - \sqrt{5} )(4 - \sqrt{5} )}{(4 - \sqrt{5)}(4 + \sqrt{5} ) } \\ \\ \sf = \frac{ {(4 + \sqrt{5}) }^{2} }{ {(4)}^{2} - {( \sqrt{5}) }^{2} } + \frac{ {(4 - \sqrt{5}) }^{2} }{ {(4)}^{2} - {( \sqrt{5}) }^{2} } \\ \\ \sf = \frac{ {(4)}^{2} + 2(4)( \sqrt{5}) + {( \sqrt{5}) }^{2} }{16 - 5} + \\ \\ \sf\frac{ {(4)}^{2} - 2(4)( \sqrt{5} ) + {( \sqrt{5}) }^{2} }{16 - 5} \\ \\ \sf = \frac{16 + 8 \sqrt{5} + 5}{11} + \frac{16 - 8 \sqrt{5} + 5}{11} \\ \\ = \frac{21 + \cancel{ 8 \sqrt{5} } + 21 - \cancel{8 \sqrt{5} }}{11} \\ \\ \sf = \frac{42}{11}$


$\large \tt HOPE \: THIS \: HELPS!!$

Answer 2

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