Question

plz give answer as soon as possible..​

Answer 1

in the numerator and denominator use the formula

(a+b)(a-b)=a2-b2

u will get

20-3=a+√15b

17=a+√15b

is the answer

brainliest?

Answer 2

Answer :-

$\sf \frac{2\sqrt{5} +\sqrt{3}}{2\sqrt{5} - \sqrt{3}} + \frac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} + \sqrt{3}} = a + \sqrt{15}b$

Rationalizing the denominator -

$\sf = \big(\frac{2\sqrt{5} +\sqrt{3}}{2\sqrt{5} - \sqrt{3}} \times \frac{2\sqrt{5} + \sqrt{3}}{2\sqrt{5} + \sqrt{3}}) + (\frac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} + \sqrt{3}} \times \frac{2\sqrt{5} - \sqrt{3}}{2\sqrt{5} - \sqrt{3}}\big)$

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

$\sf = \frac{20 + 3 + 4\sqrt{15} }{20 - 3} + \frac{ 20 + 3 - 4\sqrt{15}}{20 - 3}$

$\sf = \frac{23 + 23}{17}$

$\sf = \frac{46}{17}$

Comparing LHS and RHS -

$\sf \frac{46}{17} = a + \sqrt{15} b$

$\boxed{\sf a = \frac{46}{17}}$

$\boxed{\sf b = 0}$