# Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.] NCERT Class X Mathematics - Mathematics Chapter _Real Numbers

1
by singhSidhu428

2015-06-10T08:50:26+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

let a be any +ve integer.and it is of the form 3q,3q+1,3q+2

by euclids division algorithm;

a = bq +r, here b=3

so r=0,1,2

when r=0

a=3q

squaring both sides

a2=9q2=3(3q2)=3m

where m=3q2

when r=1

a=3q+1

squaring both sides

a2=9q2+1+6q

=3(3q2+2q)+1

=3m+1

when r=2

a=3q+2

squaring both sides

a2=9q2+4+12q

=9q2+3+1+12q

= 3(3q2+1+4q)+1

=3m+1

where m=3q2+1+4q

this shows that square of any +ve integer is either of the form 3m or 3m+1 for some integer m