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Math Help - Really hard algebra question help plz

  1. #1
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    Question n>0 and 9xsquared + kx + 36= (3x + n)squared, for all x, what is k-n?

    If n>0 and 9xsquared + kx + 36= (3x + n)squared, for all x, what is k-n?

    another question i needed to check is this one:
    '
    A family of five adults and two children are trying to cross a river. They have a lifeboat which can ONLY carry one of the following:
    A) One Child
    B) Two Children
    C) One Adult
    The boat may not carry two adults or a child and a adult
    How many one-way trips for the entire family to cross the river.
    How many one-way trips are required for a family of 1000 adults and two children

    someone plz answer im a newbie so someone help me plz
    Last edited by ianlv; September 18th 2005 at 08:57 PM.
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  2. #2
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    If 9x^2 + kx + 36 = (3x+n)^2 = (3x)^2 + 2(3x)n + n^2 then equatiing coefficients of x^2, x^1 and x^0 (ie constant term) we have 9=9 (good), k=6n and 36=n^2. So n = +- 6 and given n > 0 we have n=6 and so k=36.
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  3. #3
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    9x^2 +kx +36 = (3x +n)^2
    9x^2 +kx +36 = 9x^2 +6n +n^2
    Since the lefthand side is equal to the righthand side, then we can say their corresponding terms are equal:
    9x^2 = 9x^2 ----(1)
    kx = 6n -----(2)
    36 = n^2 -----(3)

    From (1), x = 1 -------***
    From (3), n = sqrt(36) = 6 ---***
    So plug those into (2),
    kx = 6n
    k(1) = 6(6)
    k = 36 ------***

    Therefore, (k -n) = 36 -6 = 30 -------answer.

    =====================
    River crossings.

    i) 5 Adults and 2 Children, or, 5A and 2C

    1st crossing, 2C, ---> across.
    2nd crossing, 1C, <--- crossing back.
    3rd..., 1A, ---> across. --------------1A already crossed ***
    ---------------------------
    4th..., 1C, <--- crossing back.
    5th..., 2C, ---> across.
    6th..., 1C, <--- crossing back.
    7th..., 1A, ---> across. --------------2A already crossed ***
    -------------------------------
    8th..., 1C, <--- crossing back.
    9th..., 2C, ---> across.
    10th..., 1C, <--- crossing back.
    11th..., 1A, ---> across. --------------3A already crossed ***
    -------------------------------
    12th..., 1C, <--- crossing back.
    13th..., 2C, ---> across.
    14th..., 1C, <--- crossing back.
    15th..., 1A, ---> across. --------------4A already crossed ***
    -------------------------------
    16th..., 1C, <--- crossing back.
    17th..., 2C, ---> across.
    18th..., 1C, <--- crossing back.
    19th..., 1A, ---> across. --------------5A already crossed. 1C is still left at the near side, so the 1C that has crossed will have to go back to fetch the other 1C.
    20th..., 1C, <--- crossing back.
    21st..., 2C, ---> across. -------------Now, all 5A and 2C are acrossed***

    Therefore, for the entire family of 5 adults and 2 children, 21 one-way crossings are required for all of them to cross. -----answer.

    ==========
    ii) For a family of 1000 adults and 2 children?

    As seen above where there are 5 adults and 21 crossings were required,
    (21 crossings) / (5 adults) = (4 crossings per adult) + (1 extra crossing)

    So for 1000 adults,
    (1000 adults)*(4 crossings/adult) = 4000 crossings
    4000 + 1 extra = 4001 crossings ----------------------answer.
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  4. #4
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    ty for helping me guys
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