Question

Please tell me the value of 'p' rational no. Correct answer will be marked as BRAINLIEST

Answer 1

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Answer 2

$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = p - 7 \sqrt{5} \: q \\ \\ = > \frac{(7 + \sqrt{5}) {}^{2} - (7 - \sqrt{5}) {}^{2} }{(7 - \sqrt{5})(7 + \sqrt{5}) } = p - 7 \sqrt{5} \: \: q \\ \\ = > \frac{49 + 5 + 14 \sqrt{5} - (49 + 5 - 14 \sqrt{5}) }{49 - 5} = p - 7 \sqrt{5} \: \: q \\ \\ = > \frac{49 + 5 + 14 \sqrt{5} - 49 - 5 + 14 \sqrt{5} }{44} \\ \\ = > \frac{28 \sqrt{5} }{44} = p - \sqrt{5} \: q \\ \\ = > \frac{7 \sqrt{5} }{11} = p - \sqrt{5} q \\ \\ by \: comparing \: the \: both \: sides \: on \: equation \\ \\ = > p = \frac{7}{11} and \: q = 7$

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