Question

Pls answer this. I will mark as brainliest and follow you.

Answer 1

Step-by-step explanation:

ANSWER:-

On first ,

$\frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - \sqrt{3} }$

We will do this by rationalizing it.

$\frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} }$

$= \frac{ {(2 \sqrt{5} + \sqrt{3} )}^{2} }{(2 \sqrt{5} - \sqrt{3})(2 \sqrt{5} + \sqrt{3} )}$

$\implies \: \frac{20 + 3 + 4 \sqrt{15} }{ {(2 \sqrt{5}) }^{2} - { (\sqrt{3} })^{2} }$

$\frac{23 + 4 \sqrt{15} }{17}$

The above is the first one..

Now second Factor :-

$\frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} }$

Same, as Rationalising it,

$\frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \times \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} - \sqrt{3} }$

$\implies \: \frac{ {(2 \sqrt{5} - \sqrt{3}})^{2} }{ {(2 \sqrt{5} })^{2} - { (\sqrt{3} })^{2} }$

$\frac{23 - 4 \sqrt{15} }{17}$

The above is the second one.

Now as we need to find the factor with root 15,

So we will keep it same, and our answer will be

$\frac{23 - 4 \sqrt{15} + 23 + 4 \sqrt{15} }{17}$

$\frac{46}{17}$

So a = 46/17 and b = 0.