Use euclids division lemma to show that the square of any positive integer is of the foem
Answers
Answered by
18
HI
Let a be any positive integer.
Therefore, a can be 3q or 3q+1 or 3q+2
where b = 3 and r = 0,1,2
(3q)² = 9q²
= 3(3q)²
= 3m ➡️ m = 3q²
(3q+1)² = (3q)² + 2(3q)(1) + (1)²
= 9q² + 6q + 1
= 3(3q² + 2q) + 1
= 3m + 1 ➡️m = 3q² + 2q
(3q+2)² = (3q)² + 2(3q)(2) + (2)²
= 9q² + 12q + 4
= 9q² + 12q + 3 + 1
= 3(3q² + 4q + 1) + 1
= 3m + 1 ➡️m = 3q² + 4q + 1
Therefore, the square of any positive integer is of the form 3m or 3m+1.
Hope it proved to be beneficial....
StudentTwin02:
Please mark my answer as the Brainliest ! THANKS !! ✨
Answered by
5
plz refer to this attachment
Attachments:
Similar questions