Question

If n = 5- √3 / 5+ √3 and y = 5+ √3 / 5 -√3 find n - y

Answer 1

$n = \frac{(5-\sqrt{3})}{(5+\sqrt{3})} \: --(1) \: and \\ y = \frac{(5+\sqrt{3})}{(5-\sqrt{3})}$

$Now, Value \:of \: n - y \\= \frac{(5-\sqrt{3})}{(5+\sqrt{3})} - \frac{(5+\sqrt{3})}{(5-\sqrt{3})}$

$= \frac{ (5-\sqrt{3})^{2} - (5+\sqrt{3})^{2} }{ (5+\sqrt{3})(5-\sqrt{3})}$

$= \frac { -4 \times 5 \times \sqrt{3}}{5^{2} - (\sqrt{3})^{2})}\\= \frac{-20\sqrt{3}}{25-3} \\= \frac{-20\sqrt{3}}{22} \\= \frac{-10\sqrt{3}}{11}$

Therefore.,

$\red { Value \:of \: n - y} \green {= \frac{-10\sqrt{3}}{11}}$

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