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Thread: The equation

  1. March 22nd 2008, 02:19 AM #1
    perash
    perash is offline
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    The equation

    The equation

    [x^{10}+(13x-1)^{10}=0

    has 10 complex roots

    r_1, \overline{r_1}, r_2, \overline{r_2}, r_3, \overline{r_3}, r_4, \overline{r_4}, r_5, \overline{r_5},,

    where the bar denotes complex conjugation. Find the value of

    \frac 1{r_1\overline{r_1}}+\frac 1{r_2\overline{r_2}}+\frac 1{r_3\overline{r_3}}+\frac 1{r_4\overline{r_4}}+\frac 1{r_5\overline{r_5}}.
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  2. March 24th 2008, 04:15 PM #2
    spammanon
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    The solution is 850. Use the sum and the product of the roots of a polynomial rules.
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