DeaneNicole
The sum of the squares of two consecutive positive even integers is 340. Find the integers.
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freckles
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what number comes right after n?
DeaneNicole
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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"
DeaneNicole
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Positive**
freckles
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yes i know
but what comes after n?
DeaneNicole
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I don't know!
freckles
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like for instance
if i asked you:
what comes after 1,
you would say 1+1
freckles
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if i said what comes after 2,
you would say 2+1
freckles
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if i said what comes after 3,
you would say 3+1
DeaneNicole
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So would it be n+n? or n+1??
freckles
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I'm adding 1 to each of those not n
freckles
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so n+1
freckles
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n,n+1 these are consecutive positive numbers
freckles
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of course we are assuming n is positive
freckles
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now it says the sum of the squares of these numbers
DeaneNicole
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those aren't numbers.. Those are letter o_O
freckles
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so that means
we will adding these numbers squares
DeaneNicole
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Do you know the answer to this or what??
freckles
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\[n^2+(n+1)^2=\]
It says the sum of these squares =340
so what should come after that = sign?
freckles
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I'm not gonna give you the answer
freckles
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I will guide you
freckles
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You need to solve this for n
\[n^2+(n+1)^2=340 \]
freckles
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Do you know how to solve this?
DeaneNicole
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I got
\[\chi \approx 12.5288 , -13.5288\]
DeaneNicole
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Which is in no way the answer -__-
eliassaab
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Your problem does not have integer solution.
freckles
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@eliassaab is right
DeaneNicole
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What do you mean?
freckles
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that positive number 12.5288 is not an integer
DeaneNicole
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Well duhh. That's why i need help??
freckles
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wait your question said even?
DeaneNicole
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I got the answer. its' 12 and 14. Thanks for the "help"
freckles
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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
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we add 2
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if n is the first even integer, then what is the next even integer?
freckles
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why do you have to say it like that @DeaneNicole ?
I was just trying to help
DeaneNicole
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No no no no no no no no no i didn't mean it like that!! Sorry /:
freckles
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Ok ok. Its all cool.
DeaneNicole
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Alright.
freckles
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I'm sorry I miss the word even
freckles
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all those tiny words have meaning lol
eliassaab
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You have to solve (2n)^2 + (2n+2)^2 =340
n =6
so 12 and 14
DeaneNicole
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@eliassaab we already got it.
freckles
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and @eliassaab this would have worked too
\[n^2+(n+2)^2=340 \]
eliassaab
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\[
12^2+14^2=144+196=340
\]
eliassaab
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Sorry, I did not see your post above
@DeaneNicole