The sum of the squares of two consecutive positive even integers is 340. Find the integers.

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- anonymous

The sum of the squares of two consecutive positive even integers is 340. Find the integers.

- chestercat

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- freckles

what number comes right after n?

- anonymous

That's the full question. That's all this test gave me. It says "The sum of the squares of two consecutive poistive even integers is 340. Find the Integers"

- anonymous

Positive**

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## More answers

- freckles

yes i know
but what comes after n?

- anonymous

I don't know!

- freckles

like for instance
if i asked you:
what comes after 1,
you would say 1+1

- freckles

if i said what comes after 2,
you would say 2+1

- freckles

if i said what comes after 3,
you would say 3+1

- anonymous

So would it be n+n? or n+1??

- freckles

I'm adding 1 to each of those not n

- freckles

so n+1

- freckles

n,n+1 these are consecutive positive numbers

- freckles

of course we are assuming n is positive

- freckles

now it says the sum of the squares of these numbers

- anonymous

those aren't numbers.. Those are letter o_O

- freckles

so that means
we will adding these numbers squares

- anonymous

Do you know the answer to this or what??

- freckles

\[n^2+(n+1)^2=\]
It says the sum of these squares =340
so what should come after that = sign?

- freckles

I'm not gonna give you the answer

- freckles

I will guide you

- freckles

You need to solve this for n
\[n^2+(n+1)^2=340 \]

- freckles

Do you know how to solve this?

- anonymous

I got
\[\chi \approx 12.5288 , -13.5288\]

- anonymous

Which is in no way the answer -__-

- anonymous

Your problem does not have integer solution.

- freckles

@eliassaab is right

- anonymous

What do you mean?

- freckles

that positive number 12.5288 is not an integer

- anonymous

Well duhh. That's why i need help??

- freckles

wait your question said even?

- anonymous

I got the answer. its' 12 and 14. Thanks for the "help"

- freckles

So if 2 is the first even integer then what is the next even integer?
2,2+2
right?
if 4 is the first even integer then what is the next even integer?
4,4+2
-----
we add 2
-----
if n is the first even integer, then what is the next even integer?

- freckles

why do you have to say it like that @DeaneNicole ?
I was just trying to help

- anonymous

No no no no no no no no no i didn't mean it like that!! Sorry /:

- freckles

Ok ok. Its all cool.

- anonymous

Alright.

- freckles

I'm sorry I miss the word even

- freckles

all those tiny words have meaning lol

- anonymous

You have to solve (2n)^2 + (2n+2)^2 =340
n =6
so 12 and 14

- anonymous

@eliassaab we already got it.

- freckles

and @eliassaab this would have worked too
\[n^2+(n+2)^2=340 \]

- anonymous

\[
12^2+14^2=144+196=340
\]

- anonymous

Sorry, I did not see your post above
@DeaneNicole

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