Question

plzz answer this fast with full method​

Answer 1

by division algorithm

a=bq+r

let 'a' be a positive integer, b=3

so, a=3q+r

possible remainders of 3 are 0,1,2.

(i) if r=0, a=3q+0

a=3q

squaring on both the sides

a^2=(3q)^2

a^2=9q^2

a^2=3(3q^2)

let 3q^2=m where m is any integer

a^2=3m

(ii) if r=1

a=3q+1

squaring on both the sides

a^2=(3q+1)^2

a^2=9q^2+6q+1

a^2=3(3q^2+2q)+1

Let 3q^2+2q be m

a^2=3m+1

Hope it helps you.......