Question

sum of 2 consecutive even numbers is 2096 what are the two numbers? show equation and how to solve it please, thank you!

Answer 1

2096/2 is a good start

Answer 2

no i need it like for example x(x+2)=2096 or something like that

Answer 3

hello? you there?

Answer 4

are you sure its the sum of two and not the product of two consecutive even numbers?

Answer 5

Yes the product omg thank you for correcting me!!

Answer 6

ok, so if the first number is even, then lets call it \(2x\).
then the next consecutive even number would be \(2x+2\).
so you need to solve:\[2x(2x+2)=2096\]

Answer 7

oh ok thank you but what if it was the product of 2 consecutive odd numbers?

Answer 8

odd numbers can be written as \(2x+1\)

Answer 9

isnt it the same which is 2x(x+2)?

Answer 10

\(2x\) always gives you an even number for x=1,2,3,...
\(2x+1\) always gives you and odd number for x=1,2,3,...

Answer 11

2x - 1 as well if thats easier

Answer 12

oh ok thanks, my teacher said it would be the same as an odd though?

Answer 13

so, if you are told that the product of two consecutive odd numbers is 2096, then you could write:\[(2x+1)(2x+3)=2096\]

Answer 14

oh ok thanks

Answer 15

amistre is right, \(2x-1\) is probably a better one to use.

Answer 16

what about even?

Answer 17

are we going in circles here?

Answer 18

lol.

Answer 19

even is 2x(2x+2)?

Answer 20

yes

Answer 21

okay thanks let me write that down as a note.
so 2 even consecutives is 2096 would be written as 2x(2x+2) and 2 consecutive odd would be (2x+1)(2x+3)=2096???.

Answer 22

yes, I would probably amistre's suggestion for odd numbers and use:\[(2x-1)(2x+1)=2096\]

Answer 23

*probably use

Answer 24

oh iight. okay thanks!!

Answer 25

yw