MathDB
max of M =3(ab+bc+ca)-2abc if a+b+c=3, a,b,c>=0 (HOMC 2019 JI-14)

Source:

November 7, 2020
algebrainequalitiesmax

Problem Statement

Let a,b,ca, b, c be nonnegative real numbers satisfying a+b+c=3a + b + c =3. a) If c>32c > \frac32, prove that 3(ab+bc+ca)−2abc<73(ab + bc + ca) - 2abc < 7. b) Find the greatest possible value of M=3(ab+bc+ca)−2abcM =3(ab + bc + ca) - 2abc .
Back to ProblemsView on AoPS