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Roots of Quadratic Equation

Solve : 5+√3...

Question

Solve :
$\frac{5 + \sqrt{3}}{5 - \sqrt{3}} + \frac{5 - \sqrt{3}}{5 + \sqrt{3}}$

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Solution

$\frac{5 + \sqrt{3}}{5 - \sqrt{3}} + \frac{5 - \sqrt{3}}{5 + \sqrt{3}} \frac{(5 + \sqrt{3})^{2} + (5 - \sqrt{3})^{2}}{(5 + \sqrt{3}) (5 - \sqrt{3})} \frac{25 + 3 + 30 \sqrt{3} + 25 + 3 - 30 \sqrt{3}}{25 - 3} = \frac{46}{22} = \frac{23}{11}$

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\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}} = a + \sqrt{5} b

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