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Math Help - induction problem

  1. #1
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    problem

    I have a problem but i don't know what method i should use to solve it.

    If x^3 – 2x^2 + 3x = 6 prove x=2

    Apologies for the poor format of the equation.
    Last edited by mr fantastic; August 26th 2009 at 04:08 PM. Reason: Restored deleted question.
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  2. #2
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    subtract 6 from both sides and factorize the left side:
    x^3-2x^2+3x-6 = x^2(x-2) + 3(x-2) = (x^2+3)(x-2)
    Assuming x should be a real number, this can equal to zero if and only if at least one of the brackets is zero and this happens if and only if x=2 (first bracket is never zero). In complex numbers there would be also other solutions, not only x=2.
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  3. #3
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    Quote Originally Posted by Maths Stig View Post
    I have a problem but i don't know what method i should use to solve it.

    If x^3 2x^2 + 3x = 6 prove x=2

    Apologies for the poor format of the equation.
    We will solve this using the fact that x^3 -2x^2 +3x - 6 = (x-2)(x^2+3)

    If we assume x \in \mathbb{R} (where \mathbb{R} are the real numbers), then the solution for equation would be either the solution for x-2=0 or x^2 + 3 = 0 . Obviously, x=2 is a solution, and there are no other solutions for x^2 + 3 = 0 in \mathbb{R}, thus x=2

    If you want to solve this equation over \mathbb{C} (the complex numbers), then \sqrt{3}i , -\sqrt{3}i are also solutions, but I don't think this is the case.
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