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Math Help - Quadratic Equations - help needed

  1. #1
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    Quadratic Equations - help needed

    Need help on this question:

    Solve 4y4 - 7y2 - 36 = 0
    y =




    Also need help with this question:
    Solve (square root of 3s +4) + 2s = 12
    s =


    Also need help with this question:
    Solve (square root of 17 - 2x) = (square root of 8 - x) + 1
    x =


    Also need help with this problem:
    Solve: Let u = (square root of x-2)

    (square root of x-2) squared - 12 (square root of x) + 51 = 0
    x =


    Hope someone can help.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Quadratic Equations - help needed

    For the first problem, substitute w=y^2 and then you have a quadratic equation in w, which you can easily solve. Once you find the two values for w, then y = +/- sqrt(w).

    For the next few rearrange so that you can square and get rid of the square root signs. For example starting with:
    sqrt{3s+4}+2s=12, bring the 2s term to the right and square both sides to get 3s+4=(12-2s)^2
    = 144-48s+4s^2. Now you can solve as usual.

    For the last two square both sides, and you'll end up with a square root term. Rearrange to get that term by itself, and as above square again and rearrange. Also consider doing the w=x^2 substitution to get a quadratic. Hope this helps.
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