Question

Find ‘a’ and ‘b’ if a) √5+√3√5−√3 = a-b√15

Answer 1

Answer:

a=4 and b=(-1)

Step-by-step explanation:

Given:-

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

To Find:-

a and b

Formula Used:-

(a)²-(b)²=(a+b)(a-b)

Solution:-

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

LHS:-

$\frac{\sqrt{5}+\sqrt{3} }{\sqrt{5}-\sqrt{3}}$

Rationalising the Denominator:-

$\frac{(\sqrt{5}+\sqrt{3})(\sqrt{5}+\sqrt{3}) }{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$

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

$\frac{8+2\sqrt{15} }{5-3}$

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

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

From substituting the values of a and b, we get:-

a=4 and b=(-1)