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Math Help - Algebra

  1. #1
    Member Rimas's Avatar
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    Algebra

    If:
    X+1/X=4

    then what is the value of

    X^3+1/x^3
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  2. #2
    Junior Member Dergyll's Avatar
    Joined
    Nov 2006
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    Hi

    Im just going to do this the classic/stupid way.

    Solve for x in x+1/x=4 and you get x=1/3, then substitude it into the other equation and bam you got the answer.

    THere's probably a better, more efficient way though...

    Derg
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  3. #3
    Super Member

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    Hello, Rimas!

    This problem has a spectacular solution . . .


    If x + \frac{1}{x} \,=\,4

    then what is the value of x^3 + \frac{1}{x^3}

    Cube the equation: . \left(x + \frac{1}{x}\right)^3\;=\;4^3

    We have: . x^3 + 3x^2\!\cdot\!\frac{1}{x} + 3x\!\cdot\!\frac{1}{x^2} + \frac{1}{x^3} \:= \:64\quad\Rightarrow\quad x^3 + 3x + \frac{3}{x} + \frac{1}{x^3}\:=\:64

    Then: . x^3 + 3\underbrace{\left(x + \frac{1}{x}\right)}_\downarrow + \frac{1}{x^3} \:=\:64
    . . . . . . . x^2 + 3(4) + \frac{1}{x^3} \:=\:64

    . . . . . . . . . x^3 + \frac{1}{x^3} \:=\:52

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