Question

please answer these two questions with steps.i. e. proof.
do the answers in a paper and send the image please....

Answer 1

Hope this helps you!!!!

Answer 2

answer of 1st question
$x = 9 - 4 \sqrt{5}$
$\frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \\ = \frac{9 + 4 \sqrt{5} }{(9 - 4 \sqrt{5})(9 + 4 \sqrt{5)} } \\ = \frac{9 + 4 \sqrt{5} }{ {(9)}^{2} - {(4 \sqrt{5)} }^{2} } \\ = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ = \frac{9 + 4 \sqrt{5} }{1} \\ = 9 + 4 \sqrt{5}$

$x + \frac{1}{x} = 9 - 4 \sqrt{5} + 9 + 4 \sqrt{5} \\ = 9 + 9 \\ = 18$
answer of second question
[tex] { \sqrt{ {a}^{5} } }^{ \frac{2}{5} } = { \sqrt{a} }^{5/2 \times \frac{2}{5} } = a