Question

Root2+root3/3root2-2root3=2-b r oot3

Answer 1

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = 2 - b \sqrt{3} \\ \frac{( \sqrt{2} + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} ) }{(3 \sqrt{2} - 2 \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} ) } = 2 - b \sqrt{3} \\ \frac{(6 + 2 \sqrt{6} + 3 \sqrt{6} + 6 }{18 - 12} = 2 - b \sqrt{3} \\ \frac{12 + 5 \sqrt{6} }{6} = 2 - b \sqrt{3} \\ 2 - ( \frac{ - 5 \sqrt{2 } \sqrt{3} }{6} ) = 2 - b \sqrt{3} \\ comapre \: both \\ b = \frac{ - 5 \sqrt{2} }{ 6 } \: \: \: ans$