Case deg(1)deg(1)

𝑦=3𝑥+8𝑥+2 𝑆=|𝑥+2|+|𝑦3|=|𝑥+2|+2|𝑥+2|

𝑆 is minimized when |𝑥+2|=2 via AM-GM Inequality (min𝑆=22)

Case deg(2)deg(1)

Too hard will fill in later but the idea is pretty similar—reducing to AM-GM.

Applications

References