Question

find the value of a and b if 2+√3/2-√3=a+b√3​

Answer 1

$\bf \frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ \bf \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3} \\ \\ \bf \frac{(2 + \sqrt{3} )^{2} }{(2)^{2} -( \sqrt{3} )^{2} } = a + b \sqrt{3} \\ \\ \bf \frac{4+3 + 4 \sqrt{3} }{4- 3 } = a + b \sqrt{3} \\ \\ \bf 7 + 4\sqrt{3} = a + b \sqrt{3} \\ \\ \boxed{\huge \tt{ \pmb{ \: \: \: \: a = 7 \: \: \: \: \: \: \: \: \: b = 4 \: \: \: \: }}}$