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Use euclid division Lemma to show …

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Use euclid division Lemma to show that the square of any positive integer in either of the from 3m or 3M + 1 for some integer m

Posted by Shreya Chatterjee 5 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Mansi Mishra 5 years, 6 months ago

Let x be any positive integer, then it is of the form 3q, 3q + 1 or 3q +2. Now, we have to prove that the squre of each of these can be written in the form 3m or 3m +1. Now, (3q)2=9q2=3(3q2)=3m, where m=3q2 (3q+1)2=9q2+6q+1 =3(3q2+2q)+1 = 3m + 1, where m=3q2+2q and, (3q+2q)2=9q2+12q+4 =3(3q2+4q+1)+1 = 3m + 1, where m=3q2+4q+1 Hence, the result.

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