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math-191

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show that k(x)= (5x^3) + (5/x^3) - x- (1/x)

  • math-191 - ,

    ^ sorry didn't finish: show that k(x)= k(1/x)

  • math-191 - ,

    let me rewrite k(x)

    k(x) = 5(x^3) + 5(1/x^3) - x/1 - 1/x

    it should be intuitively obvious that
    k(x) = k(1/x)

  • math-191 - ,

    yea i realize that but the question says "show" that they equal each other. im thinking possibly by some sort of identity or something.

  • math-191 - ,

    sub 1/x for x

    k(1/x) = 5(1/x^3) + 5/(1/x^3) - 1/x - 1/(1/x)
    = 5/x^3 + 5x^3 - 1/x - x

    = the original k(x) , just the order of writing down the terms has changed.

  • math-191 - ,

    ohh i see duh!! lol thanks =)

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