Question

Find the value of a and b if root3-1/root3+1+ root3+1/root3-1=a+root3 b​

Answer 1

Answer:

a=4 and b = 0

Step-by-step explanation:

Given : $\dfrac{\sqrt 3 -1}{\sqrt 3+1}+\dfrac{\sqrt 3+1}{\sqrt 3-1}=a+\sqrt 3 b$

To find, The value of a and b

Solution,

Solving LHS of the given equation,

$\dfrac{(\sqrt 3-1)^2+(\sqrt3+1)^2}{(\sqrt 3+1)(\sqrt 3-1)}=a+\sqrt 3 b$

Since,

$(a-b)^2=a^2+b^2-2ab\\\\(a+b)^2=a^2+b^2+2ab\\\\(a-b)(a+b)=a^2+b^2$

So,

$\dfrac{3+1-2\sqrt 3+3+1+2\sqrt 3}{3-1}=a+\sqrt 3 b\\\\4=a+\sqrt 3 b$

or

$4+0=a+\sqrt 3 b$

On comparing we get :

a = 4 and b = 0