Question

Prove n^2-6n+10 is always positive when n is a real number

Answer 1

n^2 - 6n + 10

Complete the square

n^2 - 6n + 10 = (n-3)^2 + 1

(n-3)^2 is always positive since any number squared is positive.

=> (n-3)^2 + 1 is always positive.