Question

Find the value of a and b, if √5+√3/√5-√3=a+b√15

Answer 1

Step-by-step explanation:

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

Now, rationalizing

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

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

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

$\frac{8 + 2 \sqrt{15} }{2} = a + b \sqrt{15}$

$\frac{2(4 + \sqrt{15}) }{2} = a + b \sqrt{15}$

$4 + \sqrt{15} = a + b \sqrt{15}$

on comparing both sides

a=4 b=1

hope this is helpful