Question

(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+b

Answer 1

hope this answer helps uh and Mark this as a brainlist answer

Answer 2

$Answer :\\ \\ Now, \\ \\ \frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } \\ \\ = \frac{(7 + \sqrt{5})(7 + \sqrt{5} ) - (7 - \sqrt{5} )(7 - \sqrt{5}) }{(7 - \sqrt{5} )(7 + \sqrt{5}) } \\ \\ = \frac{(49 + 14 \sqrt{5} + 5) - (49 - 14 \sqrt{5} + 5) }{49 - 5} ,\\ using \: \: the \: \: identity \\ (x - y)(x + y) = {x}^{2} - {y}^{2} \\ \\ = \frac{54 + 14 \sqrt{5} - 54 + 14 \sqrt{5} }{44} \\ \\ = \frac{28 \sqrt{5} }{44} \\ \\ = \frac{7 \sqrt{5} }{11} \\ \\ Given, \\ \\ \frac{7 \sqrt{5} }{11} = \frac{a \sqrt{5} }{b} \\ \\ So, \: \: a = 7 \: \: and \: \: b = 11 \\ \\ Therefore, \: \: a + b = 7 + 11 = 18$

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