prove that n^2 − 6n + 10 is always positive- completing the square Watch
My thoughts are:
(n-3)^2 will always be positive (because squared numbers are), apart from when n=3 (when the value of the bracket will be 0), in which case the "+1" makes it positive.
Is this a valid argument/line of reasoning?
n^2 - 6n + 10 = (n-3)^2 + 1 >= 1 > 0