Question

find the value of a and b​

Answer 1

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