Question

Find the values of a and



b.If √5+√3 √5−√3 = a + b√15

Answer 1

SOLUTION

$= > \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \: \: (rationalise) \\ \\ = > \frac{( \sqrt{5} + \sqrt{3}) {}^{2} }{( \sqrt{5}) {}^{2} - ( \sqrt{3} ) {}^{2} } = \frac{( \sqrt{5}) {}^{2} + ( \sqrt{3}) {}^{2} + 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3} \\ \\ = > \frac{5 + 3 + 2 \sqrt{15} }{2} = \frac{8 + 2 \sqrt{15} }{2} = a + b \sqrt{15} \\ \\ = > a = \frac{8}{2} = 4 \\ \\ = > b = \frac{2}{2} = 1$

hope it helps ☺️⬆️

Answer 2

Heya!!

Please refer to the attachment above for the solution!!

Thanks!!❤❤