Question

x=9+4√5,find √x-1/√x

Answer 1

solution,

$x = 9 + 4 \sqrt{5} \: and \: \frac{1}{x} = 9 - 4 \sqrt{5} (after \: rationalising) \\ = \sqrt{9 + 4 \sqrt{5} } - ( \sqrt{9 - 4 \sqrt{5} } \\ = \sqrt{4 \sqrt{5} } + \sqrt{4 \sqrt{5} } \\ = 4 \sqrt{5}$
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#Amrit⭐

Answer 2

(√x-1/√x)^2=x+1/x-2
x=9+4√5
1/x=x=9-4√5
(√x-1/√x)^2=9+4√5+9-4√5-2=16
√x-1/√x=+ or -4