Question

What is the answer for this question?

Answer 1

$\frac{5 + 2\sqrt{3}}{7 + 4\sqrt{3}} = \frac{(5 + 2\sqrt{3})(7 - 4\sqrt{3})}{(7 + 4\sqrt{3})(7 - 4\sqrt{3})} = \frac{35 - 20\sqrt{3} + 14\sqrt{3} - 24}{(7^2) - (4\sqrt{3})^2} \\ \\ = \frac{11 - 6\sqrt{3}}{49 - 48} = \frac{11 - 6\sqrt{3}}{1} = 11 - 6\sqrt{3} = a + b\sqrt{3}$ 

∴ a = 11 & b = -6. 

Hope this may be helpful.