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Roots of Quadratic Equation

Solve : 4+√5...

Question

Solve :
$\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}$

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Solution

$\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}} \frac{(4 + \sqrt{5})^{2} + (4 - \sqrt{5})^{2}}{(4 + \sqrt{5}) (4 - \sqrt{5})} \frac{16 + 5 + 8 \sqrt{3} + 16 + 5 - 8 \sqrt{3}}{16 - 5} = \frac{42}{11}$

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