Find the minimum value the function $f(x) = x^4 + \frac{1}{x^2}$ when $x \in \Bbb R^*$
My attempt:
Finding the minimum value of this function using calculus is a piece of cake. But since this question appeared on my test when Calculus was not taught to me, there must definitely be a way (Probably by purely using Algebra) to find the minimum value of this function without using Calculus which I am unaware of.
I tried making perfect squares but that got me nowhere. Maybe, I wasn't making the perfect, perfect square :)
Any help would be appreciated.
