Question

find the value of A in each of the following. 5+√3/7+4√3=a-√3

Answer 1

Solution:-

given by:-

$\frac{5 + \sqrt{3} }{7 + 4 \sqrt{3} } = a - \sqrt{3} \\ lhs \\ \frac{5 + \sqrt{3} }{7 + 4\sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \frac{35 + 7 \sqrt{3 } - 20 \sqrt{3} - 12 }{49 - 48} \\ 23 - 17 \sqrt{3} = a - \sqrt{3} \\ a = 23 - 17 \sqrt{3} + \sqrt{3} \\ a = 23 - 16\sqrt{3}$