Question

if A and B are two odd positive integers such that a greater than B then prove that one of the two numbers A + B by 2 and A - B by 2 is odd and the other is even​

Answer 1

$\huge\bf\pink{รσℓµƭเσɳ}$

Given, A and B are two numbers such that a>b

Let a = 2n+1, then b = 2n+3

Now $\frac{a+b}{2}=\frac{2n+1+2n+3}{2}=\frac{4n+4}{2}$

=2n+2

=2(n+1) which is even

and $\frac{a-b}{2}$=$\frac{2n+1-2n-3}{2}$=$\cancel\frac{-2}{2}$=$\LARGE\pink {-1}$ Which is odd

Hence proved.

Answer 2

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

Given, A and B are two numbers such that a>b

Let a = 2n+1

hence b = 2n+3

$\frac{a+b}{2}=\frac{2n+1+2n+3}{2}=\frac{4n+4}{2}$

= 2n + 2

Hence, 2(n+1) is even

$\frac{a-b}{2}=\frac{2n+1-2n-3}{2}=\cancel\frac{-2}{2}=-1$