Question

please do the requested questions in notebook ​

Answer 1

refer to the attachment!!!!

Answer 2

Explanation:

According to lemma:-

a=bq+r here r <or equals to r<b

All remainders are possible:-0,1,2

All integers are possible:-

a=3q+0,

a=3q+1,

a=3q+2,

A.T.Q.

Squaring both sides

(i) a^2=3q^2

a^2=3(3q)^2

m=3(3q)^2

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

a^2=a^2+2ab+b^2

a^2=oq^2+2×3q×1+1^2

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

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

m=(3q+2)

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

a^2=a^2+2ab+b^2

a^2=3q^2+2×3q×2+2^2

a^2=9q^2+12q+4

a^2=3(3q^2+4q)+4

m=(3q^2+4q)