Question

2 plus root2 by 2minus root 2 is equal to A plus B root 3

Answer 1

a+
$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \frac{\ (2 + \sqrt{3})(2 + \sqrt{3})}{(2 - \sqrt{3})(2 - \sqrt{3}) } = a + b \sqrt{3} \\ \frac{ ({2 + \sqrt{3}) }^{2} }{ {(2 - \sqrt{3}) }^{2} } \\ 3 + 2 \sqrt{3} = a + b \sqrt{3} \\ = > a = 3 \\ b = 2$