Question

a+√3b=√3+1/√3-1-√3-1/√3+1

Answer 1

first simplify

a+√3b= √3+(1/√3) -1-√3 -(1/√3) +1

+(1/√3) & -(1/√3) will cancel each other i.e the value is 0.

Similarly -1 & +1 will become 0. √3 & -√3 is 0.

The remaining terms are

a+√3b= 0.

Answer 2

$\frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 } + \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } = a + \sqrt{3} b \\ \\ \frac{( { \sqrt{3} - 1 })^{2} + ( { \sqrt{3} + 1 })^{2} }{3 - 1} = a + \sqrt{3} b \\ \\ \frac{2(3 + 1)}{2} = a + \sqrt{3} b \\ \\ 4 = a + \sqrt{3} b \\ \\ comparing \: \: both \: \: sides \\ a = 4 \: \: \: \: \: \: b = 0$