Difference between revisions of "1994 AIME Problems/Problem 13"
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The equation | The equation | ||
<center><math>x^{10}+(13x-1)^{10}=0\,</math></center> | <center><math>x^{10}+(13x-1)^{10}=0\,</math></center> | ||
− | has 10 complex | + | has 10 [[complex number|complex]] [[root]]s <math>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},\,</math> where the bar denotes complex conjugation. Find the value of |
<center><math>\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}}.</math></center> | <center><math>\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}}.</math></center> | ||
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== See also == | == See also == | ||
{{AIME box|year=1994|num-b=12|num-a=14}} | {{AIME box|year=1994|num-b=12|num-a=14}} | ||
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+ | [[Category:Intermediate Algebra Problems]] |
Revision as of 19:02, 4 December 2007
Problem
The equation
has 10 complex roots where the bar denotes complex conjugation. Find the value of
Solution
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See also
1994 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |