Question

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Answer 1

Solution :-

$\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} }$

$= \frac{(7 + 3 \sqrt{5} )(3 - \sqrt{5} ) - (7 - 3 \sqrt{5} )(3 - \sqrt{5} )}{(3 + \sqrt{5})(3 - \sqrt{5} )}$

$=\frac{( 21 - 7 \sqrt{5} + 9 \sqrt{5} - 15) - (21 - 9 \sqrt{5} + 7 \sqrt{5} - 15) }{ {3}^{2} - (\sqrt{5} ) ^{2} }$

$= \frac{ - 14 \sqrt{5} + 18 \sqrt{5} }{9 - 5}$

$= \frac{4 \sqrt{5} }{4}$

$= \sqrt{5}$

Theory used here :-

(a + b)(a - b) = a² - b²

To sum two numbers in the form of p/q, we first take the lcm of denominator and then multiply and add each term in the numerator accordingly.

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