Question

if 3 + √7 /3 - √7 = a + bv7 find the values of a and b​

Answer 1

Answer:

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7} \\ = > \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } = a + b \sqrt{7} \\ = > \frac{( {3 + \sqrt{7}) }^{2} }{ {3}^{2} - ({ \sqrt{7} )}^{2} } = a + b \sqrt{7} \\ = > \frac{ {3}^{2} + { \sqrt{7} }^{2} + 2 \times 3 \times \sqrt{7} }{9 - 7} = a + b \sqrt{7} \\ = > \frac{9 + 7 + 6 \sqrt{7} }{2} = a + b \sqrt{7} \\ = > \frac{16 + 6 \sqrt{7} }{2} = a + b \sqrt{7} \\ = > \frac{2(8 + 3 \sqrt{7}) }{2} = a + b \sqrt{7} \\ = > 8 + 3 \sqrt{7} = a + b \sqrt{7} \\ \\ on \: comparing \: \: \: we \: get \\ a = 8 \: \: \: \: \: and \: \: b = 3$