Question

√2+√3 / 3√2-2√3 = a+b√6

Answer 1

ANS.

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ = \frac{( \sqrt{2} + \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3} ) }{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3} )} \\ = \frac{6 + 2 \sqrt{6} + 3 \sqrt{6} + 6 }{18 - 12} \\ = \frac{12 + 5 \sqrt{6} }{6} \\ = 2 + \frac{5}{6} \sqrt{6} \\ = a + b \sqrt{6} \: \: \: (given) \\ \\ \\ so \\ a = 2 \: \: \: and \: \: \: b = \frac{5}{6}$

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