Question

If x=9-4V5 , find x+1/x
$9 - 4 \sqrt{5}$
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Answer 1

Answer:

18

Step-by-step explanation:

$x +\frac{1}{x} = 9 - 4 \sqrt5 + \frac{1}{9 - 4\sqrt5}\\=9 - 4 \sqrt5 +\frac{9+4\sqrt5}{(9-4\sqrt5)(9+4\sqrt5)}\\= 9 - 4\sqrt5 + \frac{9+4\sqrt5}{81-80}\\= 9 - 4\sqrt5 + 9 + 4\sqrt5\\= 18$