Answer to Question #139194 in Discrete Mathematics for Maverick

Question

Suppose a ϵ Z. Prove by contradiction that if a2 -2a + 7 is even, then a is even.

Answer 1

a2 -2a + 7 for a ϵ Z is odd sense a*2 -2*a +7 = 7

If the task condition a²-2*a+7:

a²-2*a+7 = (a-2)²+3

(a-2)²+3 is even if (a-2)² is odd

if (a-2)² is odd then a is odd

Hence the hypothesis is false and proof is not possible

Answer: proof is not possible