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anonymous

  • one year ago

Medal & Fan. The sum of the squares of 3 consecutive positive integers is 116. What are the numbers? Which of the following equations is used in the process of solving this problem? 3n^2 + 5 = 116 3n^2 + 3n + 3 = 116 3n^2 + 6n + 5 = 116

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  1. anonymous
    • one year ago
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    @hybrik

  2. freckles
    • one year ago
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    an and example of 3 consecutive positive integers is: 1,2,3 or 3,4,5 ... or (n-1),n,(n+1) we don't know what they are so let's go with the (n-1),n,(n+1) being the 3 consecutive positive integers so you have the sum of the squares of them is 116 that is (n-1)^2+n^2+(n+1)^2=116 play with the left hand side

  3. hybrik
    • one year ago
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    Freckles can do this one, I have to do something at the moment, be right back.

  4. anonymous
    • one year ago
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    2n+2+n+2n+2=116?

  5. anonymous
    • one year ago
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    probly horribly wrong

  6. freckles
    • one year ago
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    (n-1)^2 = (n-1)(n-1) do you know how to expand this?

  7. anonymous
    • one year ago
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    foil maybe?

  8. freckles
    • one year ago
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    yeah or it is just really distributing like n(n-1)-1(n-1)

  9. anonymous
    • one year ago
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    n^ 2- 2n + 1

  10. freckles
    • one year ago
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    right and we can also expand (n+1)^2 in a similar way

  11. freckles
    • one year ago
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    which should be n^2+2n+1 for (n+1)^2 so you have this now: \[(n-1)^2+n^2+(n+1)^2 =116 \\ (n^2-2n+1)+n^2+(n^2+2n+1)=116 \]

  12. freckles
    • one year ago
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    combine like terms on the left hand side

  13. anonymous
    • one year ago
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    \[-2n ^{2}+1+n^2 +2n^2+1=116\]

  14. anonymous
    • one year ago
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    not done yet

  15. freckles
    • one year ago
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    don't go any further with what you have just wrote

  16. freckles
    • one year ago
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    in the equation I wrote how many n^2 's do you see?

  17. anonymous
    • one year ago
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    3

  18. freckles
    • one year ago
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    n^2+n^2+n^2 is 3n^2

  19. freckles
    • one year ago
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    now let's look at the n's you have -2n+2n which equals ?

  20. anonymous
    • one year ago
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    n

  21. freckles
    • one year ago
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    if someone gave you 3 apples and your three all 3 apples away how many apples do you have left?

  22. anonymous
    • one year ago
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    0

  23. freckles
    • one year ago
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    if someone gave you 3 apples and your threw all 3 apples away how many apples do you have left?* yes 0

  24. freckles
    • one year ago
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    so -2n+2n is ?

  25. anonymous
    • one year ago
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    0

  26. freckles
    • one year ago
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    0 also replace 2n with 5 you have -5+5 and we know that is 0 you can also write this -2n+2n both terms have a common factor n factor the n out n(-2+2) but you should know -2+2=0 so you have n(0) but 0 times anything will result in 0 so n(0)=0 so -2n+2n=0

  27. freckles
    • one year ago
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    the last thing to add are the constant terms (the terms with out any variable)

  28. freckles
    • one year ago
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    can you show me what you think you have?

  29. anonymous
    • one year ago
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    the whole thing?

  30. freckles
    • one year ago
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    sure why not you probably want me to check the whole thing right?

  31. anonymous
    • one year ago
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    3n^2+2=0?

  32. freckles
    • one year ago
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    yep but that doesn't match any of your answers I guess they chose their 3 consecutive numbers differently maybe they chose n,n+1,n+2 which also works \[n^2+(n+1)^2+(n+2)^2=116 \\ n^2+n^2+2n+1+n^2+4n+4=116 \\ 3n^2+6n+5=116 \]

  33. freckles
    • one year ago
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    you can choose the three consecutive integers in many ways

  34. freckles
    • one year ago
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    that is solving either one of the equations will result in the same 3 consecutive integers

  35. anonymous
    • one year ago
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    thanks again

  36. freckles
    • one year ago
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    though I like my equation better because it seems simpler to solve :p

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