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  1. Paris la ville de l'amour
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    anemone's Avatar
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    #1
    Here is this week's POTW:

    -----

    Let $a$ and $b$ be non-zero real numbers such that $a^3+3a^2b^2+b^3=a^3b^3$.

    Find all the possible values of $\dfrac{1}{a}+\dfrac{1}{b}$.

    -----

    Remember to read the to find out how to !

  2. Pessimist Singularitarian
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    #2
    Hello, MHB Community!

    anemone has asked me to fill in for her while she is away on holiday.

    Congratulations to to following users for their correct submissions:


    Honorable mention goes to lfdahl for a partially correct solution.

    castor28's solution follows:


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