Question

If x = 9 + 4√5 , find the value of x + 1/x

Answer 1

Answer:

$\frac{10 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } }$

Step-by-step explanation:

look the picture

Answer 2

Answer:

$\huge\bf{18}$

Step-by-step explanation:

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