Question

Find the value ofa&b if7+√5/7-√5-7-√5/7+√5==a+7√5/11 b

Answer 1

$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = a + \frac{7 \sqrt{5} }{11} b \\ \frac{( {7 + \sqrt{5} })^{2} - ( {7 - \sqrt{5} })^{2} }{ {7}^{2} - ( { \sqrt{5} })^{2} } = a + \frac{7 \sqrt{5} }{11} b \\ \frac{14 \sqrt{5} + 14 \sqrt{5} }{49 - 5} = a + \frac{7 \sqrt{5} }{11} b \\ \frac{28 \sqrt{5} }{44} = a + \frac{7 \sqrt{5} }{11}b \\ \frac{7 \sqrt{5} }{11} = a + \frac{7 \sqrt{5} }{11} b \\ comparing \: both \: sides \\ a = 0 \: \: \: \: b = 1$