Question

if a = 5 - 2 under root 6 find under root a - 1/ under root a

Answer 1

$a = 5 - 2 \sqrt{6} \\ \frac{1}{a} = \frac{1}{5 - 2 \sqrt{6} } = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } = \frac{5 + 2 \sqrt{6} }{25 - 24} = 5 + 2 \sqrt{6} \\ now \: let \: .\sqrt{a} - \frac{1}{ \sqrt{a} } = x \\ squaring \: both \: the \: sides \\ = { ( \sqrt{a} - \frac{1}{ \sqrt{a} } )}^{2} = {x}^{2} \\ = {x}^{2} = a + \frac{1}{a} - 2 \\ = {x}^{2} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} - 2 \\ = {x}^{2} = 10 - 2 \\ = x = \sqrt{8} \\ = x = 2 \sqrt{2}$
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