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Maths Alert!!!

Ask questions of CBSE Class X and discuss the same here. For any doubts relates to CBSE Class X.

Maths Alert!!!

Postby Shrestha » Mon Mar 16, 2009 8:34 pm

Question. Use Euclid"s division lemma to show that the square of any positive integer is either of the form 3m or 3m+1.
[Hint: x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square of these and show that they can be rewritten in the form 3m or 3m+1.]

Ans. An integer can be of the form 3q, 3q+1 or 3q+2. Square all of these integers.
Shrestha
 
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Joined: Thu Mar 12, 2009 7:05 pm

Re: Maths Alert!!!

Postby shubhangi_d23 » Fri Oct 23, 2009 11:04 am

let a b any +ve integer and let b= 3.
using euclid's div. algorithm, a= bq+r or a= 3q+r, where 0 is less thn or equal to r which is less thn b.
therefore, r can take values: 0, 1, 2 (since b=3)

for, r=0:
a= 3*q + 0
a= 3q
a= 3m (where q is some integer, m)

for, r= 1
a= 3*q + 1
a= 3q + 1
a= 3m + 1 (where q is some integer m)

v can also take our (3m+2), but we won't.... since it is not asked in quesion..
shubhangi_d23
 
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