Question

5+2√3/7+4√3 = a-6√3​

Answer 1

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a - 6 \sqrt{3} \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{7 {}^{2} - (4 \sqrt{3} ) {}^{2} } = a - 6 \sqrt{3} \\ \frac{11 - 6 \sqrt{3} }{49 - 48} = a - 6 \sqrt{3} \\ 11 - 6 \sqrt{3} = a - 6 \sqrt{3}$

On comparing

we get

$a = 11$