Question

Please answer the following question....

Too much for my brain

Answer 1

Option (2)

Given:

$= = > \: \: a = \frac{ \sqrt{5} + 1 }{ \sqrt{5} - 1} \\ \\ = = > \: \: a = \frac{ \sqrt{5} + 1}{ \sqrt{5} - 1} \times \frac{ \sqrt{5} + 1 }{ \sqrt{5} + 1 } \\ \\ = = > \: \: a = \frac{ {( \sqrt{5} + 1)}^{2} }{ {( \sqrt{5}) }^{2} - {(1)}^{2} } \\ \\ = = > \: \: a = \frac{ 5 + 1 + 2 \sqrt{5} }{5 - 1} \\ \\ = = > \: \: a = \frac{2(3 + \sqrt{5} )}{4} \\ \\ = = > \: \: a = \frac{3 + \sqrt{5} }{2}$

and

$= = > \: \: b = \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1 } \\ \\ = = > \: \: b = \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1} \times \frac{ \sqrt{5} - 1 }{ \sqrt{5} - 1 } \\ \\ = = > \: \: b = \frac{ {( \sqrt{5} - 1)}^{2} }{ {( \sqrt{5}) }^{2} - {(1)}^{2} } \\ \\ = = > \: \: b = \frac{5 + 1 - 2 \sqrt{5} }{4} \\ \\ = = > \: \: b = \frac{2(3 - \sqrt{5} )}{4} \\ \\ = = > \: \: b = \frac{3 - \sqrt{5} }{2}$

Now,

a = (3 + √5)/ 2 ; b = (3 - √5)/2

Refer to the attachment.