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09Use division algorithm to show that the square of any positive integer is ofthe form3p or 3p+1.cricofthe forme |
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Answer» Hope it HELPS you!! Let the positive INTEGER-a b-3 If b - 3 so 0= R < b R =0, 1,2 q= some integer By using division algorithm let r =0 a=bq+r a =3q + 0 a=3q squaring both side a^ =(3q) ^ a^= 9q^ a^=3(3q^) let P= 3q^ a^ = 3P ____________1 Let r = 1 a=bq+ r a= 3q + 1 squaring both side a^= (3q+1) ^ a^=(3q)^ + (1) ^ + 2 ×3q×1 a^ =9q^ +1+6q a^= 9q^+6q+1 a^=3(3q^+2q) +1 let 3q^+2q = P a^=3p+1________________2 From EQ 1 and 2 we can say that the SQUARE of any positive integer is in the form of 3q and 3q+1 . But if you are a cbse student ,then you must know that this part is removed from exam point of view. Thankyou |
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