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  1. MHB Master
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    #1
    Here is this week's POTW:

    -----

    Monic quadratic polynomials $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-23,\,-21,\,-17$ and $-15$ and $Q(P(x))$ has zeros at $x=-59,\,-57,\,-51$ and $-49$. What is the sum of the minimum values of $P(x)$ and $Q(x)$?

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    Remember to read the "POTW submission guidelines to find out how to "submit your answers!

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  3. MHB Master
    MHB Math Helper
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    anemone's Avatar
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MHB Challenges Award (Jul-Dec 2013)
    #2 Thread Author
    Hi MHB,

    I was told by castor28 that this week's POTW (High School) was a duplicate of POTW #363, which is true. I am truly sorry for letting this thing happened. I therefore want to thank him for catching the mistake.

    Please let me make it up by presenting to you the following problem:

    A geometric sequence $(a_n)$ has $a_1=\sin x,\,a_2=\cos x$ and $a_3=\tan x$ for some real number $x$. For what value of $n$ does $a_n=1+\cos x$?

    -----

    Remember to read the "POTW submission guidelines to find out how to "submit your answers!

  4. MHB Master
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MHB Challenges Award (2015)  

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MHB Challenges Award (Jul-Dec 2013)
    #3 Thread Author
    Congratulations to the following members for their correct answer!

    1. castor28
    2. MegaMoh

    Solution from castor28:


    Alternate solution from MegaMoh:

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