Give a proof by Mathematical Induction of the following:
For all integers n>=3, (n^2 - 3n + 2) is positive.
The Attempt at a Solution
Hey guys, this is a problem from my discrete mathematics study guide. Here's what I got so far:
Basis step: If n=3, then LHS=3 and RHS = (3^2 - 3(3) + 2) = 2 -> positive
Induction: Assume that (n^2 - 3n + 2) is positive for arbitrary n>=3
Now I'm not sure about how to actually go about the proof. I understand that we then show the induction hypothesis working for n+1 but I'm not sure how to put this together.
Something like: (n+1)^2 - 3(n+1) + 2 = n^2 - n....
EDIT: I see, so then using (n^2 - n) and plugging in 3 I get (3^2 - 3 = 6) which is equal to (4^2 - 3(4) + 2 = 6) -> positive. Would this be a complete proof?