Question

plz solve this fast​

Answer 1

$\huge{ \sf{ \orange{ \mid{ \underline{ \overline{ \pink{work \: out...}}}}}}}$

$\large{ \bold{ \red{ \underline{ \underline{Question...}}}}}$

$\large{ \sf{ \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = a + b \sqrt{6} }}$

$\large{ \bold{ \green{ \underline{ \underline{Solution...}}}}}$

$\large{ \sf{ \red{rationalizing \: denominator \: first..}}} \\ \\ \large{ \sf{ \to \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } }} \\ \\ \large{ \sf{ \to \: \frac{ (\sqrt{2} + \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3} ) }{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3} ) } }} \\ \\ \large{ \sf{ \to \: \frac{6 + 3 \sqrt{6} + 2 \sqrt{6} + 6 }{(3 \sqrt{2}) {}^{2} - (2 \sqrt{3}) {}^{2} } }} \\ \large{ \sf{by \: using \: (a - b)(a + b) = {a}^{2} - b {}^{2} }} \\ \\ \large{ \sf{ \to \: \frac{12 + 5 \sqrt{6} }{18 - 12} }} \\ \\ \large{ \sf{ \to \: \frac{ 12 + 5 \sqrt{6} }{6} }} \\ \\ \large{ \sf{ \to \: \frac{12}{6} + \frac{5 \sqrt{6} }{6} }} \\ \\ \large{ \sf{ \to \: 2 + \frac{5 \sqrt{6} }{6} }} \\ \large{ \sf{ \green{by \: comparing \: a + b \sqrt{6} }}}... \\ \\ \large{ \sf{ \boxed{ \red{ \to \: a = 2 \: \: \: \: b = \frac{5}{6} }}}}$

$\large{ \blue{ \bold{required \: answer...}}}$

$\large{ \bold{ \orange{ nothing \: beats \: a \: great \: smile...}}} \\ \large{ \bold{ \orange{ so \: keep \: smililing \: always...}}}$