Question

simplify 10 and 11 questions

Answer 1

>>>>>>>>>>(★)<<<<<<<<<<<<

SoLuTiOn

>>>>>>>>>>>(★)<<<<<<<<<<<<<

11)

$\frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} - \sqrt{7} } = a + b \sqrt{14} \\ \\ < rationalise > \\ \\ \frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} - \sqrt{7} } \times \frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} + \sqrt{7} } = > \frac{2 + 7 + 2 \sqrt{14} }{2 - 7} \\ \\ = > \frac{9 + 2 \sqrt{14} }{ - 5} \\ \\ by \: comparision.... \\ \\ a = 9 \: \: an \: b = 2$

>>>>>>>>>>>>>(★)<<<<<<<<<<<<<<<
10 )

1)
$\frac{2 + 3 \sqrt{6} }{3 + \sqrt{6} } \times \frac{3 - \sqrt{6} }{3 - \sqrt{6} } \\ \\ = > \frac{6 + 9 \sqrt{6} - 2 \sqrt{6 } - 18}{9 - 6} \\ \\ = > \frac{7 \sqrt{6} - 12}{3}$

2)
$\frac{3 \sqrt{2} - 2 \sqrt{3} }{ \sqrt{2 \times 2 \times 2} + \sqrt{3 \times 3 \times 3} } = \frac{3 \sqrt{2 } - 2 \sqrt{3} }{2 \sqrt{2} + 3 \sqrt{3} } \times \frac{2 \sqrt{2} - 3 \sqrt{3} }{2 \sqrt{2} - 3 \sqrt{3} } \\ \\ = > \frac{12 - 4 \sqrt{6} - 9 \sqrt{6} + 18}{8 - 27} \\ \\ = > \frac{6 - 13 \sqrt{6} }{19}$