Question

if a and b are two odd positive integer such that a greater than b ,than prove two numbers a+b ÷2 and a-b÷2 is odd and the other is even​

Answer 1

Answer:

let a = 2x + 3 and let b = 2x + 1

where x is a positive integer and a is greater than b

(a+b)/2 = (2x+3+2x+1)/2 = (4x + 4)/2 = 2x + 2

2x + 2 is even for any positive integer since 2x +2 is divisible by 2 to give x + 1

(a-b)/2 = (2x+3-2x-1)/2 = (2)/2 = 1

1 is odd

so if a and b are two odd positive integer such that a greater than b

then a + b /2 always even

a-b / 2 always negative

Step-by-step explanation: