Question

If root 3-1/ root 3 +1= a+b root 3 find the value of a and b class 9

Answer 1

Hi friend, hereis your answer

Ans:- First you have to rationalize the denominator by multiplying both numerator and denominator with root 3-1

then you will get{ root 3 + 1 }2/{root 3}2- {1}2

that will be = 4+2*root3  /2

2{2+root 3 } / 2{1}

and finally you are left with 2+root3

therefore, a = 2 and b =1


Hope this helps.

Answer 2

Answer:

$a=2,b=-1$

Step-by-step explanation:

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

To find: Values of a & b.

Rationalize the denominator in LHS we have:

$\frac{\sqrt{3}-1}{\sqrt{3}+1 }*\frac{\sqrt{3}-1 }{\sqrt{3}-1 } =a+b\sqrt{3}$

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

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

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

Now comparing both sides we have:

$a=2,b=-1$

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