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djmccarter
22.02.2022 •
Mathematics
 The square of an odd number is always odd
Try Examples with three odd numbers to check this conjecture And find where it’s false
Do you believe it’s true or false
Explain why it’s true or false
Solved
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Ответ:
True
Step-by-step explanation:
3² = 9 ⇒ odd
7² = 49 ⇒ odd
9² = 81 ⇒ odd
Therefore, the square of an odd number is always odd.
Proof
If n is an odd number, it can be written as n = 2k + 1, for some integer k.
Therefore, n² = (2k + 1)²
= 4k² + 4k + 1
= 2(2k² + 2k) + 1
As 2(2k² + 2k) + 1 is odd, this proves that the square of an odd number is always odd.
Ответ: