Question

Find the value of a and b if
5+√3
____ =a+b√3
7-4√3

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{5 + \sqrt{3} }{ 7 - 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{5 \times 7 + 5 \times 4 \sqrt{3} + \sqrt{3} \times 7 + \sqrt{3} \times 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3} })^{2} } \\ \\ = \frac{35 + 20 \sqrt{3} + 7 \sqrt{3} + 12}{49 - 48} \\ \\ 47 + 27 \sqrt{3} = a + b \sqrt{3} \\ \\ a = 47 \\ \\ b = 27$


Hope this helps!!!!

@Mahak24

Thanks....
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