Given that $a^2 + b^2 + c^2 = 6\;$, determine the minimum value of $ab + bc + ca\;$.
I know that $a^2 + b^2 + c^2 ≥ ab + bc + ca\;$, so that means $6 ≥ ab + bc + ca\;$, but I don't know where to go from there.
Given that $a^2 + b^2 + c^2 = 6\;$, determine the minimum value of $ab + bc + ca\;$.
I know that $a^2 + b^2 + c^2 ≥ ab + bc + ca\;$, so that means $6 ≥ ab + bc + ca\;$, but I don't know where to go from there.