Question

if √(5)+√(3)/√(5)−√(3)=a+b√15 find the value of a and b

Answer 1

(√5 + √3)^2 / (√5)^2 -(√3)^2
5+3+2√15/ 5-3
8+2√15 /2
4+√15=a+ b√15
a=4
b=1

Answer 2

Hi...☺

Here is your answer....✌

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } = a + b \sqrt{15} \\ \\LHS \\ \\= \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ =\frac{{( \sqrt{5})}^{2} + {( \sqrt{3}) }^{2} + 2 \times \sqrt{5} \times \sqrt{3} }{{( \sqrt{5})}^{2} - {( \sqrt{3} )}^{2} } \\ \\ =\frac{5 + 3 + 2 \sqrt{15} }{5 - 3} \\ \\ =\frac{8 + 2 \sqrt{15} }{2}\\ \\= 4 + \sqrt{15}$

Now,
We have

4 + √15 = a + b√15

By comparing
We get,

a = 4 , b = 1