Question

if2+√3÷2+√3=a+b√3 find the value of a and b

Answer 1

$\textit{ \textbf{ Hello Mate! }}$

$\frac{ 2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3}$

Rationalize, go though once attatchment.
( above in app, below through web )

$\boxed{ \textsf{ Hence,\:a=7\:and\:b=4 }}$

Have great future ahead!

Answer 2

Hello!

$\dfrac{2+\sqrt{3}}{2-\sqrt{3}} = \sf a+b\sqrt{3} \\ \\ \implies \dfrac{2+\sqrt{3}}{2-\sqrt{3}} \times \dfrac{2+\sqrt{3}}{2+\sqrt{3}} = \sf a+b\sqrt{3} \\ \\ \implies \dfrac{(2+\sqrt{3})^{2}}{(2)^{2}-(\sqrt{3})^{2}} = \sf a+b\sqrt{3} \\ \\ \implies \dfrac{4+3+4\sqrt{3}}{4-3} = \sf a+b\sqrt{3} \\ \\ \implies 7 + 4\sqrt{3} = \sf a + b\sqrt{3}$

On Comparin'

$\star \: \bf{a = 7} \\ \star \: \bf{b = 4}$

Hence,
The values of a and b are $7$ and $4$ respectively.

Cheers!