Question

find the value of a and b.​

Answer 1

Answer:

We will solve it through rationalization:

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

$= > \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } = a + b \sqrt{7}$

$= > \frac{(3 + \sqrt{7}) {}^{2} }{(3) {}^{2} - (\sqrt{7}) } {}^{2} = a + b \sqrt{7}$

$= > \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} = a + \sqrt{7}$

$= > \frac{16 + 6 \sqrt{7} }{2} = a + b \sqrt{7}$

$= > \frac{8 + 3 \sqrt{7} }{1} = a + b \sqrt{7}$

$= > 8 + 3 \sqrt{7} = a + b \sqrt{7}$

Therefore,

$a = 8 \: \: \: \: and \: \: \: b = 3$