Maths quiz?

Question

If a=1/(2-root3)
what is a-1/a
(use surd for this)

Answer

a=1/(2-root3)
what is a-1/a?

First from the ‘definition’ above we get,
a=1/(2-root3)
= [1*(2+root3) ] /[ (2-root3)*(2+root3) ]
= [1*(2+root3) ] /[ (4-3 ]
=2+root3

and using a=1/(2-root3), just ‘inverting places’ we find,
1/a = (2-root3)

Now.

a – 1/a = 2+root3 – [ (2-root3) ]
= 2 root3