You probably haven't solved a quartic equation like this before!

I was trying to find the maximum of f(x)=1/((2-x)^2+1)+1/(x^2+1). After taking the derivative and setting it equal to zero, I encountered this quartic equation. At first glance, this quartic equation is not factorable, but after further investigation, I found a nice way to solve it. Shop the Xmas Three sweatshirt: https://amzn.to/4geMKCE ---------------------------------------- Big thanks to my Patrons for the full-marathon support! Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Jordan T Batman 1127 Mathguru Дмитрий П 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 ---------------------------------------- #blackpenredpen #math #calculus #apcalculus