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Write whether the square of any positive integer can be the form 3m+2, where m is a natural number.Justify your answer

Posted by Adharsh Anilkumar 6 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 8 months ago

No.
Justification:
Let a be any positive integer.
Then by Euclid’s division lemma, we have a
= bq + r, where 0 ≤ r < b
For b = 3, we have
a = 3q + r, where 0 ≤ r < 3 ...(i)
So, The numbers are of the form 3q, 3q + 1 and 3q + 2.
So, (3q)² = 9q² = 3(3q²)
= 3m, where m is a integer.
(3q + 1)² = 9q²+ 6q + 1
= 3(3q²+ 2q) + 1
= 3m + 1, where m is a integer.
(3q + 2)² = 9q² + 12q + 4, which cannot be expressed in the form 3m + 2.
Therefore, Square of any positive integer cannot be expressed in the form 3m + 2.

0Thank You

Devansh Yadav 6 years, 8 months ago

Let n be any orbitory number

0Thank You

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CBSE > Class 10 > Mathematics