Question

anyone pls answer my question. its urgent.​

Answer 1

Here is your answer @sreelakshmi

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

Answer 2

$\green{ \fcolorbox{grey}{grey}{ \checkmark \: \textsf{Verified \: answer}}}$

$\begin{gathered} \frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{ {(2 + \sqrt{3} )}^{2} }{ {2}^{2} - { \sqrt{3} }^{2} } = a + b \sqrt{3} \\ \\ \frac{7 + 4 \sqrt{3} }{4 - 3} = a + b \sqrt{3} \\ \\ {7 + 4 \sqrt{3} }= a + b \sqrt{3} \\ \\ {\boxed{ \rm \: a = 7} }\\ \boxed{ \rm b = 4}\end{gathered}$