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

1 Answer

7 votes

Answer:

a=4 and b = 0

Explanation:

Given :
(\sqrt 3 -1)/(\sqrt 3+1)+(\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,


((\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,


(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

User Martin Klinke
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