Question

if 5+root3/7-4root3=94a+3root3b find a and b

Answer 1

your answer is
$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } = 94a + 3 \sqrt{3} b \\ \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } = 94a + 3 \sqrt{3} b \\ \frac{35 + 12 + 7 \sqrt{3} + 20 \sqrt{3} }{49 - 48} = 94a + 3 \sqrt{3} b \\ 47 + 27 \sqrt{3} = 94a + 3 \sqrt{3} b \\ 94a = 47 \: \: and \: \: 3 \sqrt{3} b = 27 \sqrt{3} \\ a = 2 \: \: and \: \: b = 9$