- #1
Nipuna Weerasekara
- 36
- 2
Homework Statement
Let ##x\in \mathbb{R} ##
Prove the conditional statement that,
if ## x>-1## then ## x^2 + \frac {1}{x^2+1} \geq 1##
2. The attempt at a solution
Suppose ## x>-1## is true.
Then ## x^2>1##
Then ## \frac{1}{2}>\frac {1}{x^2+1}##
Then ##x^2+ \frac{1}{2}>x^2+\frac {1}{x^2+1}##
After that I have no clue how to get to the part where ## x^2 + \frac {1}{x^2+1} \geq 1## happens. Pls help...