## DeaneNicole 3 years ago The sum of the squares of two consecutive positive even integers is 340. Find the integers.

1. freckles

what number comes right after n?

2. DeaneNicole

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"

3. DeaneNicole

Positive**

4. freckles

yes i know but what comes after n?

5. DeaneNicole

I don't know!

6. freckles

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

7. freckles

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

8. freckles

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

9. DeaneNicole

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

10. freckles

I'm adding 1 to each of those not n

11. freckles

so n+1

12. freckles

n,n+1 these are consecutive positive numbers

13. freckles

of course we are assuming n is positive

14. freckles

now it says the sum of the squares of these numbers

15. DeaneNicole

those aren't numbers.. Those are letter o_O

16. freckles

so that means we will adding these numbers squares

17. DeaneNicole

Do you know the answer to this or what??

18. freckles

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

19. freckles

I'm not gonna give you the answer

20. freckles

I will guide you

21. freckles

You need to solve this for n $n^2+(n+1)^2=340$

22. freckles

Do you know how to solve this?

23. DeaneNicole

I got $\chi \approx 12.5288 , -13.5288$

24. DeaneNicole

Which is in no way the answer -__-

25. eliassaab

Your problem does not have integer solution.

26. freckles

@eliassaab is right

27. DeaneNicole

What do you mean?

28. freckles

that positive number 12.5288 is not an integer

29. DeaneNicole

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

30. freckles

31. DeaneNicole

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

32. 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?

33. freckles

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

34. DeaneNicole

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

35. freckles

Ok ok. Its all cool.

36. DeaneNicole

Alright.

37. freckles

I'm sorry I miss the word even

38. freckles

all those tiny words have meaning lol

39. eliassaab

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

40. DeaneNicole

41. freckles

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

42. eliassaab

$12^2+14^2=144+196=340$

43. eliassaab

Sorry, I did not see your post above @DeaneNicole