Question

answer this question on time​

Answer 1

Answer:

your first answer is in the image

and your second answer is 6 -2√5

Answer 2

(a)

$\frac{4 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{4 - 3 \sqrt{5} }{3 - \sqrt{5} } \\ = \frac{(4 + 3 \sqrt{5})(3 - \sqrt{5}) - (4 - 3 \sqrt{5} )(3 + \sqrt{5}) }{ {3}^{2} - { ( \sqrt{5} )}^{2} } \\ = \frac{12 - 4 \sqrt{5} + 9 \sqrt{5} - 75 - 12 - 4 \sqrt{5} + 9 \sqrt{5} + 75}{9 - 5} \\ = \frac{ - 8 \sqrt{5} + 18 \sqrt{5} }{4} \\ = \frac{10 \sqrt{5} }{4} \\ = \frac{5 \sqrt{5} }{2}$

(b)

$x = \frac{1}{2 + \sqrt{5} } \\ \\ {x}^{2} + 4x + 1 \\ \\ { (\frac{1}{2 + \sqrt{5} }) }^{2} + 4(2 + \sqrt{5)} + 1 \\ \\ = \frac{1}{4 + 5 + 4 \sqrt{5} } + 8 + 4 \sqrt{5} + 1 \\ \\ = \frac{1}{9 + 4 \sqrt{5} } + 4 \sqrt{5} + 9 \\ \\ = \frac{1 + {(9 + 4 \sqrt{5})}^{2} }{9 + 4 \sqrt{5} } \\ \\ = \frac{1 + 81 + 80 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ = \frac{162 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ = \frac{18(9 + 4 \sqrt{5}) }{9 + 4 \sqrt{5} } \\ \\ = 18$