Question

if x = 5+2 root 6 then find x - 1/x

Answer 1

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Answer 2

$x = 5 + 2 \sqrt{6}$

$\dfrac{1}{x} = \dfrac{1}{5 + 2 \sqrt{6}}$

$\dfrac{1}{x} = \dfrac{1}{5 + 2 \sqrt{6}} \times \dfrac{5 - 2 \sqrt{6}}{5 - 2 \sqrt{6}}$

$\dfrac{1}{x} =\dfrac{5 - 2 \sqrt{6}}{(5)^2 - (2 \sqrt{6})^2}$

$\dfrac{1}{x} =\dfrac{5 - 2 \sqrt{6}}{25 - 24}$

$\dfrac{1}{x} =\dfrac{5 - 2 \sqrt{6}}{1}$

$\dfrac{1}{x} =5 - 2 \sqrt{6}$

$x + \dfrac{1}{x} = 5 + 2 \sqrt{6} - (5 - 2 \sqrt{6})$

$x + \dfrac{1}{x} = 5 + 2 \sqrt{6} - 5 + 2 \sqrt{6}$

$x + \dfrac{1}{x}= 4\sqrt{6}$