{"status": "success", "data": {"description_md": "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 $$ \\frac 1{r_1\\overline{r_1}}+\\frac 1{r_2\\overline{r_2}}+\\frac 1{r_3\\overline{r_3}}+\\frac 1{r_4\\overline{r_4}}+\\frac 1{r_5\\overline{r_5}}. $$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The equation <span class=\"katex--display\"> x^{10}+(13x-1)^{10}=0 </span> has 10 complex roots <span class=\"katex--inline\">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},</span> where the bar denotes complex conjugation. Find the value of <span class=\"katex--display\"> \\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}}. </span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "1994 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/94_aime_p14", "prev": "/problem/94_aime_p12"}}