Question

Prove that x+1/x is greater than or equal to 2 or less than or equal to -2?

Answer 1

(x-1)^2 >= 0 because its perfect square

x^2 -2x +1 >=0

x^2 + 1 >= 2x

(x^2 +1)/x >=2

x + 1/x >=2