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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 (A+B)/2 and (A-b)/2 is Odd and the Other is Even. - Mathematics

If a and b are two odd positive integers such that a > b, then prove that one of the two numbers `(a+b)/2`and`(a-b)/2` is odd and the other is even.

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Solution

Let a = 2q + 3 and b = 2q + 1 be two positive odd integers such that a > b

Now, `(a+b)/2=(2q+3+2q+1)/2=(4q+4)/2=2q+2=`an even number

and `(a-b)/2=((2q+3)-(2q-1))/2=(2q+3-2q-1)/2=2/2=1=`an odd number

Hence one of the two numbers `(a+b)/2` and `(a-b)/2` is odd and the other is even for any two positive odd integer.

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.1 | Q 1 | Page 10
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