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If a and b are both odd integers
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01 Oct 2018, 15:50
01 Oct 2018, 15:50
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If \(a\) and \(b\) are both odd integers which of the following must be even.
Indicate all possible values.
A. \((a-b)(a^2+ab+b^2)\)
B. \(a^b +b^a\)
C. \(b^2+3ab+b^2\)
D. \(a^3 + b^3 + 3ab(a+b)\)
Indicate all possible values.
A. \((a-b)(a^2+ab+b^2)\)
B. \(a^b +b^a\)
C. \(b^2+3ab+b^2\)
D. \(a^3 + b^3 + 3ab(a+b)\)
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Re: If a and b are both odd integers
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02 Jan 2019, 08:25
02 Jan 2019, 08:25
2
sandy wrote:
If \(a\) and \(b\) are both odd integers which of the following must be even.
Indicate all possible values.
A. \((a-b)(a^2+ab+b^2)\)
B. \(a^b +b^a\)
C. \(b^2+3ab+b^2\)
D. \(a^3 + b^3 + 3ab(a+b)\)
Indicate all possible values.
A. \((a-b)(a^2+ab+b^2)\)
B. \(a^b +b^a\)
C. \(b^2+3ab+b^2\)
D. \(a^3 + b^3 + 3ab(a+b)\)
A quick approach is to plug in ODD values for a and b.
The easiest ODD value to work with is 1.
So, let's evaluate each answer choice by replacing a and b with 1.
We get:
A. \((1-1)(1^2+(1)(1)+1^2) = 0\) EVEN
B. \(1^1+1^1 = 1+1 = 2\) EVEN
C. \(1^2+3(1)(1)+1^2 = 1+3+1 = 5\) ODD
D. \(1^3 + 1^3 + 3(1)(1)(1+1) = 1 + 1 + 6 = 8\) EVEN
Answer: A, B, D
Cheers,
Brent
Re: If a and b are both odd integers
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26 Jul 2024, 21:13
26 Jul 2024, 21:13
I am a bit confused. Shouldn't we plug in negative values of these as well since the question stem does not specify if a and b are "positive" odd integers? a and b could very well be -1 in which case option (B) might not hold true
