Question

A positive integer is of the form 3q +1 being a natural number. Can you write its square in any form other than 3m+1 i.e. 3m or 3m+2 for some integer m?justify your answer ​

Answer 1

Answer:

Step-by-step explanation:

$(3q+1)^{2}$ = $9q^{2} + 6q + 1$ $= 3(3q^{2} +2q) +1 =3m+1$

or

$9q^{2} + 6q + 1 = 9q^{2} + 6q + 4 - 3 = 3(3q^{2} + 2q - 1) +4 => 3m +4$

or

$9q^{2} + 6q + 9 -8 = 3(3q^{2} + 2q +3) - 8 = 3m -8$

so, basically, if u write 1 as the difference of 3q and 3q+1/ 3q and 3q-1,

u can have different forms.