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Math Help - Quadratic equation question

  1. #1
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    Quadratic equation question

    If m is a solution of x^2=2x-1, show that
    i) m^3=3m-2
    ii) m^4 - m^2=2m-2.
    The question did not ask us to find the value of m. And I do not think the solution would ibe finding the value of m and substituting it back and do the LHS=RHS approach.
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  2. #2
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    Quote Originally Posted by musmd View Post
    If m is a solution of x^2=2x-1, show that
    i) m^3=3m-2
    ii) m^4 - m^2=2m-2.
    The question did not ask us to find the value of m. And I do not think the solution would ibe finding the value of m and substituting it back and do the LHS=RHS approach.
    i) m^2 = 2m - 1.

    Therefore:

    m^3 = 2m^2 - m ..... (1)

    2m^2 = 4m - 2 \Rightarrow 2m^2 - m = 3m - 2 .... (2)

    Substitute (2) into (1) and it's blue sky all the way.


    ii) Use a similar technique. You might need to use the result found in i).
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