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Ncert exemplar solutions

CHAPTERS

A positive integer is of the form 3q + 1, q being a natural number. In which of the following can you write its square other than 3m + 1?

Consider the positive integer 3q + 1, where q is a natural number.

(3q + 1)^2 = 9q^2 + 6q + 1 \\ = 3(3q^2 + 2q) + 1 \\= 3m + 1, (where m is an integer which is equal to 3q² + 2q.

Thus (3q + 1)^2 cannot be expressed in any other form apart from 3m + 1.

Consider the positive integer 3q + 1, where q is a natural number.

(3q + 1)^2 = 9q^2 + 6q + 1 \\ = 3(3q^2 + 2q) + 1 \\= 3m + 1, (where m is an integer which is equal to 3q² + 2q.

Thus (3q + 1)^2 cannot be expressed in any other form apart from 3m + 1.

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