PROOF OF

( X+1/X) > or = 2 , for a>0 and

equality holds for a=1.

using AM >= GM

( X+1/X)./2 >= (X*(1./X))^1/2

( X+1/X) >= 2*1

or
(X+1/X) >= 2

useArithmetic Mean is always ≥Geometric Mean.

We can write:

(x+1/x )/2≥x⋅1/x

Thus,x+1/x more thsan equal to 2 but this is true when x>0
but if its less than zero
AM<GM
then x+1/x will be less than equal to 2