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Math Help - determining the value of K

  1. #1
    rcs
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    determining the value of K

    the Given K^2-3K+5 = 0
    determine the value of K^4-6K^3+9K^2-7.

    if i were to solve this ... i will use the quadratic formula to solve the K. and if the value of K is solve then i will plug in to the expression K^4-6K^3+9K^2-7. Am i doing it right? if not please Guide me on this ...

    Thank you and God Bless
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    Re: determining the value of K

    Yes that's correct, but there's a much faster way that doesn't involve using a calculator. Square the first equation:

    (k^2 - 3k + 5)^2 = 0^2

    k^4 - 6k^3 + 19k^2 - 30k + 25 = 0

     \Rightarrow (k^4 - 6k^3 + 9k^2 - 7) + 10k^2 - 30k + 32 = 0

     \Rightarrow (k^4 - 6k^3 + 9k^2 - 7) + 10(k^2 - 3k + 5) - 28 = 0

    And since k^2 - 3k + 5 = 0, we have

    (k^4 - 6k^3 + 9k^2 - 7) - 28 = 0. The desired expression is equal to 28.
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  3. #3
    rcs
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    Re: determining the value of K

    from the bottom of my heart... a million thanks to you sir..
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