Question

If a=√3+1/√3-1 and b =√3-1/√3+1 so a²+ab-b²=? ​

Answer 1

Answer:

Rationalise the denominator of a and b

a=(√3+1)(√3+1)/(√3-1)(√3+1)

a= (√3+1)^2/(√3)^2-1

a= 3+1+2√3/3-1

a= 4+2√3/2

a= 2(2+√3)/2

a= 2+√3

b=(√3-1)(√3-1)/(√3+1)(√3-1)

b= (√3-1)^2/(√3)^2-1

b= 3+1-2√3/3-1

b= 4-2√3/2

b= 2(2-√3)/2

b= 2-√3

Now, a^2+ab-b^2= (2+√3)^2-(2-√3)^2+(2+√3)(2-√3)

= (2+√3+2-√3)(2+√3-2+√3)+2^2-√3^2

= 4(2√3)+4-3

= 8√3+1