Question

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

Answer:

Step-by-step explanation: by euclid's division lemma,

a=bq + r

let b=3

=> r= 0, 1 or 2

therefore,

a=3q + 2

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

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

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

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

Hope it helps

Answer 2

Note: the numbers after variables are their powers

It is necessary to solve all the values of r in the exam

Answer:

Step-by-step explanation:

By using Euclid's Division Lemma, a=bq+r

Where, 0 ≤ r < b here, b=3 therefore, r= 0,1 or 2

So,

1. .......r= 0

2. .......r= 1

(skipping to r= 2 NOT TO BE DONE IN EXAM)

3. r= 2

a2= (3q+2)^2

a2= 9q2 + 12q + 4

a2= 3(3q2 + 4q) + 4

Now, let (3q2 + 4q) be m

Therefore, a2= 3m + 4

I HOPE IT HELPS.....