Question

plzz solve ques 10 3rd part plzz

Answer 1

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Answer 2

$LHS \\ = \frac{3 \sqrt{2 } - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{3 \sqrt{2 } - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \times \frac{3 \sqrt{2 } - 2 \sqrt{3}}{3 \sqrt{2 } - 2 \sqrt{3}} + \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{ {(3 \sqrt{2} - 2 \sqrt{3})}^{2} }{ {(3 \sqrt{2}) }^{2} - {(2 \sqrt{3}) }^{2} } + \frac{6 + 2 \sqrt{6} }{3 - 2} \\ = \frac{18 - 12 \sqrt{6} + 12 }{18 - 12} + 6 - 2 \sqrt{6} \\ = \frac{30 - 12 \sqrt{6} }{6} + 6 + 2 \sqrt{6} \\ = 5 - 2 \sqrt{6} + 6 + 2 \sqrt{6} \\ = 11 \\ = RHS \\ Hence \: proved.$