Proof that and give two example in words (explain) of the following proposition

Question

Proof that and give two example in words (explain) of the following proposition If x^2 -8x +7 is even then x is odd

Explanation / Answer

=> x^2 - 8x + 7 => x^2 - 7x - x + 7 => x(x - 7) - 1(x - 7) => (x - 7) * (x - 1) we are given that (x - 7) * (x - 1) is even then (x - 7) must be even and (x - 1) must be even given (x - 7) is even, then x is odd given (x - 1) is even, then x is odd so, if x^2 - 8x + 7 is even then x is odd. Examples: --------- 1) take an odd value for x. x = 1 then x^2 - 8x + 7 is 0 which is even. 2) take an odd value for x. x = 3 then x^2 - 8x + 7 is -8 which is even. so, given x^2 - 8x + 7 is even then x is odd.

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