Question

(√2+2√3)/(2√2+√3)= a+b√6 find the values of a and b

Answer 1

Given (2+√3)/(2 -√3) = a + b√3
Multiply and divide with (2 -√3)

On comparing both the sides, we get
a= 7 and b = 4

Answer 2

Hello Mate!

$\frac{ \sqrt{2} + 2 \sqrt{3} }{2 \sqrt{2} + \sqrt{3} } \times \frac{2 \sqrt{2} - \sqrt{3} }{2 \sqrt{2} - \sqrt{3} } \\ \frac{( \sqrt{2} + 2 \sqrt{3} )(2 \sqrt{2} - \sqrt{3} )}{(4 \times 2) - 3} \\ \frac{4 - \sqrt{6} + 4 \sqrt{6} - 6 }{8 - 3} \\ \frac{ - 2 - 2 \sqrt{6} }{5} = a + b \sqrt{6} \\ a = \frac{ - 2}{5} \\ b = \frac{ - 2}{5}$


Hope it helps☺!