Hello everyone, does anybody know: how to prove that for any number of x is the real inequality. my calculations below, but i didn’t have the idea what shall i do next

Let . Then



If calculus methods are okay, consider the function . Then has a critical point where vanishes, i.e.



The second derivative is



and at this critical point, we have a value of

. The derivative test for extrema indicates this is the site of a minimum, and we get a minimum value of



as desired.

Hnmmmn not sure