Math, asked by Anonymous, 8 months ago

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Answered by BihariSwag
31

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Answered by sandlisingh76
1

Answer:

Let a be a positive integer

Then, by Euclid division lemma

a = bq +r

Therefore, a = 3q +r - (1)

0 <r<b

0<r<3

r = 0,1,2

For, r =0

a = 3q

Squaring on both sides

a2 = 9 q 2

a2 = 3 × 3q 2

Since, a2 = 3m

Therefore, a2 = 3 m

For, r=1

a = 3 q +1

Squaring on both sides

a2 = (3q +1)2

a2 =9q2 + 6q +1

= 3 (3q2 + 2q) +1

m = 3q 2 + 2 q

a 2 = 3m +1

For, r = 2

a = 3 q + 2

Squaring on both sides

a 2 = ( 3 q + 2) 2

a2 = 9q2 + 12 q + 4

= 9 q 2 + 12 q + 3 + 1

= 3 ( 3 q 2 + 4 q + 1) + 1

m= 3q 2 + 4q + 1

a2 = 3m + 2

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