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blondinia [14]
3 years ago
11

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

Mathematics
1 answer:
Digiron [165]3 years ago
4 0

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

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