1985 OIM Problems/Problem 3
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Problem
Find the roots , , , and of the equation: knowing that they're all real, positives and that:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
By Vieta's, . Because the roots are real and positive, by AM-GM, \frac{r_1}{2}=\frac{r_2}{4}=\frac{r_3}{5}=\frac{r_4}{8}=\frac14(r_1,r_2,r_3,r_4)=\boxed{(\frac12,1,\frac54,2)}$.