This is a problem given in an exam for middle-schoolers going to high school in Vietnam. It is not easy though.
Given that a≥1,b≥1,c≥ and ab+bc+ac=K where K is a constant ≥3, find with proof, the maximum value of a2+b2+c2
Given that a≥1,b≥1,c≥ and ab+bc+ac=K where K is a constant ≥3, find with proof, the maximum value of a2+b2+c2
