Question

plzz answer it...

It's urgent!!!!​

Answer 1

a=31 and b = 10

1. we will rationalize 5-root6 / 5+ root6
2. we will get (5 - root 6)sq./ (5)sq. - (root6)sq.
3. it will be 25 + 6 - 10 root 6./19
4. 31 - 10 root 6/19
5. on comparing we will get: a = 31 and b = 10

Answer 2

Step-by-step explanation:

BTP,

$\frac{5 - \sqrt{6} }{5 + \sqrt{6} } =a + b \sqrt{5} \\ = > \frac{5 - \sqrt{6} }{5 + \sqrt{6} } \times \frac{5 - \sqrt{6} }{5 - \sqrt{6} } = a + b \sqrt{5} \\ = > \frac{ {(5)}^{2} - 2 \times 5 \times \sqrt{6} + { (\sqrt{6} )}^{2} }{ {(5)}^{2} - { (\sqrt{6}) }^{2} } = a + b \sqrt{6} \\ = > \frac{25 - 10 \sqrt{6} + 6}{25 - 6} = a + b \sqrt{6} \\ = > \frac{31 - 10 \sqrt{6} }{19} = a + b \sqrt{6}$

Comparing both sides, we get,

a = $\frac{31}{19}$

and,

$b \sqrt{6} = \frac{ - 10 \sqrt{6} }{19} \\ = > b = \frac{ - 10}{19}$