Question

PLEASE ANSWER THIS ASAP

Answer 1

Answer:

$a = 2 \\ b = \frac{5}{6}$

Step-by-step explanation:

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2\sqrt{3} } = a + b \sqrt{6} \\ \\ = > \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } = a + b \sqrt{6} \\ \\ = > \frac{( \sqrt{2} + \sqrt{3}) \times (3 \sqrt{2} + 2 \sqrt{3}) }{(3 \sqrt{2)}^{2} - {(2 \sqrt{3} })^{2} } = a + b\sqrt{6} \\ \\ = > \frac{ \sqrt{2}(3 \sqrt{2} + 2 \sqrt{3)} + \sqrt{3}(3 \sqrt{2} + 2 \sqrt{3} ) }{(9 \times 2) - (4 \times 3)} =a + b \sqrt{6} \\ \\ = > \frac{(3 \sqrt{2} \times \sqrt{2 } ) +( 2 \sqrt{3} \times \sqrt{2} ) + (3 \sqrt{2} \times \sqrt{3}) + (2 \sqrt{3} \times \sqrt{3} )}{18 - 12} = a + b\sqrt{6} \\ \\ = > \frac{6+ 2 \sqrt{6} + 3 \sqrt{6} +6 }{6} = a + b \sqrt{6} \\ \\ = > \frac{12 + 5 \sqrt{6} }{6} =a + b \sqrt{6} \\ \\ = > \frac{12}{6} + \frac{5 \sqrt{6} }{6} =a + b \sqrt{6} \\ = > 2 + \frac{5}{6} \sqrt{6} = a + b \sqrt{6}$

so a = 2 and b = 5/6 hope it helps.