# Thread:

1. ## 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

$\frac 1{r_1\overline{r_1}}+\frac 1{r_2\overline{r_2}}+\frac 1{r_3\overline{r_3}}+\frac 1{r_4\overline{r_4}}+\frac 1{r_5\overline{r_5}}$.

2. The solution is 850. Use the sum and the product of the roots of a polynomial rules.
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