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Math Help - solving equations

  1. #1
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    solving equations

    Solve the following algebraically
    a)x^3+5x^2=2x+6
    b)x^4-13x^2=-36
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  2. #2
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    Quote Originally Posted by william View Post
    Solve the following algebraically
    a)x^3+5x^2=2x+6
    b)x^4-13x^2=-36
    a) x^3 + 5x^2 - 2x - 6 = 0

    Notice that f(-1) = (-1)^3 + 5(-1)^2 - 2(-1) - 6 = -1 + 5 + 2 - 6 = 0

    So by the factor and remainder theorems, x + 1 is a factor.

    Using long division, you should find that

    f(x) = (x + 1)(x^2 + 4x - 6) = 0

    By the null factor law

    x + 1 = 0 or x^2 + 4x - 6 = 0

    The first equation is easy to solve, the second is solved using the Quadratic Formula.

    So x = -2 - \sqrt{10}, x = -1, x = -2 + \sqrt{10} are the solutions.
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  3. #3
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    Quote Originally Posted by william View Post
    Solve the following algebraically
    a)x^3+5x^2=2x+6
    b)x^4-13x^2=-36
    b) x^4 - 13x^2 + 36 = 0

    Notice that if I write X = x^2 the equation becomes

    X^2 - 13X + 36 = 0

    (X - 4)(X - 9) = 0

    X = 4 or X = 9.


    Since X = x^2

    x^2 = 4 or x^2 = 9

    So x = -3, x = -2, x = 2, x = 3 are the solutions.
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