Question

Rationalize the
denominator and find the value of a and b
5+√7/5-√7=a+b√7
​

Answer 1

$\frac{5 + \sqrt{7} }{ 5 - \sqrt{7} } = a + b \sqrt{7} \\ \frac{5 + \sqrt{7} }{5 - \sqrt{7} } \times \frac{5 + \sqrt{7} }{5 + \sqrt{7} } = a + b \sqrt{7} \\ \frac{( {5 + \sqrt{7} })^{2} }{25 - 7} = a + b \sqrt{7} \\ \frac{25 + 7 + 10 \sqrt{7} }{18} = a + b \sqrt{7} \\ \frac{32 + 10 \sqrt{7} }{18} = a + b \sqrt{7} \\ \frac{16 + 5 \sqrt{7} }{9} = a + b \sqrt{7} \\ \frac{16}{9} + \frac{5}{9} \sqrt{7} = a + b \sqrt{7} \\ comparing \: both \: sides \\ a = \frac{16}{9} \: \: \: \: \: b = \frac{5}{9}$