Question

find two consecutive positive even numbers the sum of whose squares is 340.

Answer 1

Okay.. word problems... the first step is always to represent values... and how do you represent two consecutive even numbers?

Answer 2

lol i have no idea

Answer 3

Two consecutive even numbers... if we let the first one be x, what's the next even number?

Answer 4

y

Answer 5

in terms of x, of course. It is harder to work with two unknowns.

Answer 6

yeah well i have no idea how to do this because in the lesson it never taught any of this

Answer 7

Maybe it did and you didn't catch it?
LOL
Ok... example... if we have the even number 4... what's the next even number?

Answer 8

6

Answer 9

okay... another... the even number 30... what's the next one?

Answer 10

32

Answer 11

good... see, every time, you just add 2, don't you?

Answer 12

yes now how do i get that answer lol

Answer 13

So... if x is an even number, what is the next?

Answer 14

anther even number

Answer 15

yeah.... what do you add to x so that you get the next even number?

Answer 16

x^2

Answer 17

No... I mean, what do you add to x to get the next even number?
What did you add to 4 to get 6?
What did you add to 30 to get 32?

Answer 18

add 2 so it would be x+2

Answer 19

338+2?
lol

Answer 20

Good.
So your two consecutive even numbers are x and x+2,
Understood? :)

Answer 21

yeah

Answer 22

So... the sum of the squares of x and (x+2)

Answer 23

yep lol thats where im gona be lost

Answer 24

What's the square of x?

Answer 25

x^2

Answer 26

good... and the square of (x+2) ?

Answer 27

(x+2)^2

Answer 28

So, their sum...
\[\large x^2 +(x+2)^2 = ?\]
is what?

Answer 29

340

Answer 30

okay...
\[\large x^2 + (x+2)^2=340\]
Now we can start solving.

Answer 31

14,12?

Answer 32

It's not 14.
Try again :D

Answer 33

Are you using quadratic formula?

Answer 34

oh no lol duhh

Answer 35

it still comes out to 12,-14

Answer 36

yeah, -14.
Not 14

So between those two, which is your answer for x?
There can be only one.

Answer 37

12

Answer 38

because i need two positives

Answer 39

and 12+2 is 14

Answer 40

Impressive.
I see you only needed to get started and the rest comes smoothly, no? :)

Answer 41

yeah exactly what i needed

Answer 42

Well, nicely done.

Answer 43

thanks buddy :)