Question

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Answer 1

Here's your answer for the question
There is a printing mistake in the question hope it will be helpful.

Answer 2

Hi...☺

Here is your answer...✌

Given that,

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } = 94a + 3 \sqrt{3} b \: \: \: \: \: \: .....(1) \\ \\ Rationalising \: the \:LHS \: we \: get \\ \\ \frac{5 + \sqrt{3} }{7 - 4 \sqrt{ 3} } = \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ = \frac{35 + 20 \sqrt{3} + 7 \sqrt{3} + 12}{ {7}^{2} -{(4 \sqrt{ 3} ) }^{2} } \\ \\ = \frac{47 + 27 \sqrt{3} }{49 - 48} \\ \\ = \frac{47 + 27 \sqrt{3} }{1} = 47 + 27 \sqrt{3} \\ \\from \: (1) \: we \: have \\ \\ 47 + 27 \sqrt{3} = 94a + 3 \sqrt{3} \: b \\ \\ by \: compairing \: we \: get \\ \\47 = 94a \implies a = \frac{1}{2} \\ and \\ 27 \sqrt{3} = 3 \sqrt{3} \: b\implies b = 9$