Question

if a = 2+√5/2-√5 and b = 2-√5/2+√5, then find the value of a2-b2

Answer 1

a^2 - b^2
= (2+√5/2 -√5)^2 - (2-√5/2 + √5)^2
=(2+√5(1/2-1))^2 - (2- √5(1/2-1))^2
=(2-√5/2)^2 - (2+√5/2)^2
= 2^2 + (√5/2)^2 - 2×2×√5/2 -2^2 - (√5/2)^2 -2×2× √5/2
= - 2(2×2× √5/2) = - 4√5

you can also solve by ,
a^2 - b^2 = (a+b) (a-b)
answer will be the same.....even lite bit easily done ....
I hope this will help you....