Question

(√5+√3)/(√5-√3)=a+√15b . find a,bp

Answer 1

Answer:

we should first rationalise it

(8+2 root 15 ) / 2 = a + root 15 b

4 + root 15  

so compare both sides  

a=4

b=1

Step-by-step explanation:

Answer 2

The value of a and b for the given is 4 and 1.

Solution:

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

Rationalizing means the process of rationalizing the denominator, by rewriting the denominator for make the denominator into rational numbers.

Rationalizing the above equation so that,  

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

[By multiplying $\sqrt{5}+\sqrt{3}$ in both numerator and denominator of the LHS of equation]

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

[Since $(a+b)^{2}=a^{2}+b^{2}+2 a b$

$(a+b)(a-b)=a^{2}+b^{2}]$

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

$\frac{8+2 \sqrt{15}}{(2)}=a+\sqrt{15} b$

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

$4+\sqrt{15} \times 1=a+\sqrt{15} b$

By Comparing both side of the equations, then we get:

a= 4;b = 1