Question

Why we take 2x+1 and 2x+3 in two consecutive odd numbers?

Answer 1

Because x is any natural number

and on multiplying any natural number with two..
we always gets an even number...

So to make the result odd we add 1
to it..
and for other we add 3 to it..


for example..
if value of x=3

then 2x=2(3)
=6 ;which is an even
and
to make the result odd
we add 1 to it..

i.e,
6+1=7

but to get next odd consecutive we can't add 2 to it..
because 6+2=8;which is an even

so we add 3 to get next odd consecutive number
i.e, 6+3=9;which is odd

hope it helps