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If a and b are two …

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If a and b are two odd positive integers such that a>b then prove that one of the two numbers is odd and other even

Posted by Silla Ranjeet 1 year, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Rudra Pratap Singh 1 year, 7 months ago

We have a and b are two odd positive integers such that a & b but we know that odd numbers are in the form of 2n+1 and 2n+3 where n is integer. so, a=2n+3, b=2n+1, n∈1 Given ⇒ a>b now, According to given question Case I: 2 a+b = 2 2n+3+2n+1 = 2 4n+4 =2n+2=2(n+1) put let m=2n+1 then, 2 a+b =2m ⇒ even number. Case II: 2 a−b = 2 2n+3−2n−1 2 2 =1 ⇒ odd number. Hence we can see that, one is odd and other is even.

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