Question

Root 5 + root 3 / root 5 - root 3 =a+b root 7

Answer 1

Step-by-step explanation:

I think it should as b√15.

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

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

$\frac{5 + 3 + 2 \sqrt{15}}{5 - 3} = a + b \sqrt{15} = > \frac{8 + 2 \sqrt{15} }{2} =$

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

Hence a=>4 and b=>1. Hope it helps you.

Answer 2

Answer:

a = 4 and b = 1

Step-by-step explanation:

$L.H.S \: = \: \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

Rationalizing the denominator we get:

$= \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = \frac{ {( \sqrt{5} )}^{2} + {( \sqrt{3} )}^{2} + 2. \sqrt{5}. \sqrt{3} }{ {( \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3} \\ \\ = \frac{8 + 2 \sqrt{15} }{2} \\ \\ \bf = 4 + \sqrt{15}$

4 + √15 = a + b√15

a = 4 and b = 1