This is a problem given in an exam for middle-schoolers going to high school in Vietnam. It is not easy though.
Given that $a \ge 1, b \ge 1, c \ge$ and $$ab + bc + ac = K$$ where $K$ is a constant $\ge 3$, find with proof, the maximum value of $$a^2 + b^2 + c^2$$
Given that $a \ge 1, b \ge 1, c \ge$ and $$ab + bc + ac = K$$ where $K$ is a constant $\ge 3$, find with proof, the maximum value of $$a^2 + b^2 + c^2$$
