Question

please answer with full solution​

Answer 1

Answer:

see attached file for your answer

Answer 2

$\frac{ \sqrt{5} + 1}{ \sqrt{5} - 1 } + \frac{ \sqrt{5} - 1 }{ \sqrt{5} + 1 } \\ = \frac{ {( \sqrt{5} + 1) }^{2} + {( \sqrt{5} - 1) }^{2} }{( \sqrt{5} - 1)( \sqrt{5} + 1) } \\ = \frac{5 + 1 + 2 \sqrt{5} + 5 + 1 + 2 \sqrt{5} }{ { (\sqrt{5} )}^{2} - {1}^{2} } \\ = \frac{12 + 4 \sqrt{5} }{5 - 1} \\ = \frac{4(3 + \sqrt{5} )}{4} \\ = 3 + \sqrt{5}$