Question

answers me faster.......

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

Answer 1

Let a be 2.

b be 2.

Then ; 2 , 2 both are positive integers.......( given )

According to the given condition ;


$2 + 3 \div 2$
Hence , 1 + 3 = 4 , which is an even number.

$2 - 3 \div 2$

Also , 3 is only left alone, which is an odd number.

HOPE IT HELPS YOU.............!!!

Answer 2

thanks for saying the correct question.
if both a and b are odd, they can be represented as,
a=2m+1
b=2n+1
so,
(a+b)/2=(2m +1+2n+1)/2=m+n+1
(a-b)/2=(2m+1-2n-1)/2=m-n

case 1
if m and n are odd integers,
m+n+1 is surely odd
m-n is surely even

case 2
if any one of m and n is odd and other is even,
m+n+1 is even
m-n is odd

case 3
if both m and n are even integers,
m+n+1 is odd
m-n is even
hope this helps
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