Question

find the value of a and b if

5+root6 divided by 5-root 6=a+b root6

please explain me .

Answer 1

Hello Mate!

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

Hope it helps!☺

Answer 2

hope it will helpful for you

please mark me brainlist