Question

√5+√3/√5-√3=a+b√5 find a
a and b

Answer 1

HERE'S YOUR ANSWER......✌️✌️

Answer 2

Heya !!!

Here is the answer.

Given :
$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } = a + b \sqrt{5}$
Lets rationalize the denominator...
$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = > \frac{ {( \sqrt{5} + \sqrt{3}) }^{2} }{{ ( \sqrt{5} ) }^{2} - {( \sqrt{3}) }^{2} } \\ = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} \\ = > \frac{8 + 2 \sqrt{15} }{2} (taking \: 2 \: as \: common) \\ = > \frac{2(4+ \sqrt{15} )}{2}$
$= > 4 + \sqrt{15}$

Now, Comparing With RHS...
$4 + \sqrt{15} = a + b \sqrt{5}$
a = 4 and
b√5 = √15
=> b = √15/√5 = √3

Hence, a = 4 and b=√3

Hope You Got It