For any integer m, square of the number is of the form ______ or ______(a) 3m + 3, 3m – 2(b) 3m – 2, 3m + 2(c) 3m + 2, 3m – 3(d) 3m, 3m + 1I got this question in an online interview.Enquiry is from Euclid’s Division Lemma in portion Real Numbers of Mathematics – Class 10

For any integer m, square of the number is of the form ______ or _____

1.	For any integer m, square of the number is of the form ______ or ______(a) 3m + 3, 3m – 2(b) 3m – 2, 3m + 2(c) 3m + 2, 3m – 3(d) 3m, 3m + 1I got this question in an online interview.Enquiry is from Euclid’s Division Lemma in portion Real Numbers of Mathematics – Class 10
Answer» Correct option is (d) 3m, 3m + 1 Easiest explanation: LET a be any arbitrary number. Then, by Euclid’s division LEMMA, a = 3q + r where 0 ≤ r ≤ 3 a^2 = (3q + r)^2 = 9q^2 + r^2 + 6qr When r = 0, Then, a^2 = 9q^2 + 0^2 + 6q(0) = 9q^2 = 3(3q^2) = 3m where m = 3q^2 Now, r = 1 a^2 = (3q+r)^2 = 9q^2 + (1)^2 + 6q(1) = 9q^2 + 1 + 6q = 3(3q^2 + 2Q) + 1 = 3m + 1 where m = 3q^2 + 2q When r = 2, a^2 = (3q+r)^2 = 9q^2 + (2)^2 + 6q(2) = 9q^2 + 12q + 4 = 3(3q^2) + 3(4)q + 3 × 1 + 1 = 3[(3q^2) + (4)q + 1] + 1 = 3m + 1 where m = (3q^2) + (4)q + 1 Hence, square of number n is of the form 3m or 3m + 1

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For any integer m, square of the number is of the form or (a) 3m + 3, 3m – 2(b) 3m – 2, 3m + 2(c) 3m + 2, 3m – 3(d) 3m, 3m + 1I got this question in an online interview.Enquiry is from Euclid’s Division Lemma in portion Real Numbers of Mathematics – Class 10

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