Question

if $\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3} = a + \sqrt{15}b$
find the values of A and B.

Answer 1

HELLO DEAR,


$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = \frac{ {( \sqrt{5} + \sqrt{3} )}^{2} }{ { \sqrt{5} }^{2} - \sqrt{3} ^{2} } \\ \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3} \\ \\ = \frac{ 8 + 2 \sqrt{15} }{2} \\ \\ \frac{2(4 + \sqrt{15}) }{2} \\ \\ = 4 + \sqrt{15} - - - (1)l.h.s$
now comparing it with R.H.S

WE GET,

A=4 AND B = 1


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hello :D


here the Value of a => 4 and the value of b=> 1



hope it helps you dear !!


thanks