Question

if:

x- {1/x}=√18

prove that: x+ {1/x}=√18/2 +-√22/2

Answer 1

$x - \frac{1}{x} = \sqrt{18} \\ take \: squre \: both \: side \\ {(x - \frac{1}{x}) } ^{2} = 18 \\ {(x + \frac{1}{x} )}^{2} - 2x( \frac{1}{x} ) = 18 \\ {(x + \frac{1}{x}) }^{2} - 2 = 18 \\ {(x + \frac{1}{x}) }^{2} = 22 \\ {(x + \frac{1}{x} )} = + - \sqrt{22} \:$

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