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Mello

  • 3 years ago

Simplify the following

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  1. Mello
    • 3 years ago
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    |dw:1347334599772:dw|

  2. CliffSedge
    • 3 years ago
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    There isn't much you can do with that. You can try factoring. There's a difference of cubes up top, and the bottom is a square of sorts.

  3. Mello
    • 3 years ago
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    @CliffSedge I know that the answer should be 2013. I have no idea how to get there though

  4. CliffSedge
    • 3 years ago
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    Just to make sure we're looking at the same thing, is this what you wrote? \[\frac{8-27^n}{4+2 \cdot 3^n +9} \space +2011+3^n\]

  5. Mello
    • 3 years ago
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    yup

  6. CliffSedge
    • 3 years ago
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    Well if the answer is 2013, then \[\frac{8-27^n}{4+2 \cdot 3^n +9} +3^n = 2.\]

  7. Mello
    • 3 years ago
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    Is it possible to add 2^2 to 2?

  8. CliffSedge
    • 3 years ago
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    The top can be factored as a difference of cubes: \[8-27^n = 2^3-3^{3n} = (2-3^n)(4+2 \cdot 3^n+3^{2n})\]

  9. CliffSedge
    • 3 years ago
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    What do you mean, "add 2^2 to 2?" 2^2 = 4, 4+2=6.

  10. CliffSedge
    • 3 years ago
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    Are you sure that denominator isn't 4+2*3^n+9^n ?

  11. CliffSedge
    • 3 years ago
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    Then it would work out just fine.

  12. Mello
    • 3 years ago
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    @CliffSedge Im sure, its just 9.

  13. CliffSedge
    • 3 years ago
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    \[\frac{8-27^n}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[\frac{2^3-3^{3n}}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[\frac{(2-3^n)((4+2 \cdot 3^n +9^n)}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow\] \[2-3^n +2011+3^n =2013.\]

  14. CliffSedge
    • 3 years ago
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    Well, that's unfortunate.

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