Question

Prove that x^2 + 1/x^2 >= 2

Answer 1

multiply by x^2
set equal to 0

\[x^{4} -2x^{2} +1 \ge 0\]

Factor
\[(x^{2} -1)^{2} \ge 0\]
this is True , everything squared is greater than 0
thus original statement is True

Answer 2

Thank you!

Answer 3

or go other way round
we know that anything squared is always >=0

A^2 > = 0
put A = x+1/x
solve