Question

87. If √3+√2/√3-√8 = a + b√6, then find out the value of a and b?​

Answer 1

a=-5 and b=0

hope it help

Answer 2

Answer:

To Find:- value of a & b

Solution:-

First solve L.H.S

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{8} }$

Rationalize

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{8} } \times \frac{ \sqrt{3} + \sqrt{8} }{ \sqrt{3} + \sqrt{8} } \\ = \frac{ \sqrt{9} + \sqrt{24} + \sqrt{6} + \sqrt{16} }{ \sqrt{3}^{2} - \sqrt{ {8}^{2} } } \\ = \frac{3 + 2 \sqrt{6} + \sqrt{6} + 4 }{3 - 8} \\ = \frac{7 + 3 \sqrt{6} }{ - 5} \\ = \frac{ - (7 + 3 \sqrt{6} )}{5}$

We can separate it as

$\frac{ - 7}{5} + \frac{ - 3 \sqrt{6} }{ 5}$

And

R.H.S = a+b√6

comparing Both side

we get

$a = \frac{ - 7}{5} \\ b = \frac{ - 3 \sqrt{6} }{5}$

Hope it helps

Hit The Brainliest if you find it helpful