Question

If both a & b are rational numbers find the values of a & b in √5+√3/√5-√3 = A+B√15

Answer 1

Hey User!!!

given :- $\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3} =a+b\sqrt15$

$\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3} \\ \\=> \frac{\sqrt5+\sqrt3}{\sqrt5-\SQRT3} * \frac{\sqrt5+\sqrt3}{\sqrt5+\sqrt3}\\ \\=> \frac{(\sqrt5+\sqrt3)(\sqrt5+\sqrt3)}{(\sqrt5-\sqrt3)(\sqrt5+\sqrt3)} \\ \\ =>\frac{(\sqrt5)^{2}+2(\sqrt5)(\sqrt3)+(\sqrt3)^{2}} {(\sqrt5)^{2}-(\sqrt3)^{2}} \\ \\=>\frac{5+2\sqrt15+3}{25-9}$

$=> \frac{8+2\sqrt15}{16} \\ \\ => \frac{4+1\sqrt15}{8} \\ \\ => \frac{4}{8} + \frac{1}{8}\sqrt15$

hence a = 1/2 and b = 1/8

Cheers!!!