1987 OIM Problems/Problem 5

Problem

If $r$, $s$, and $t$ are all the roots of the equation: \[x(x-2)3x-7)=2\]

(a) Prove that $r$, $s$, and $t$ are all postive

(b) Calculate: arctan $r$ + arctan $s$ + arctan $t$.

Note: We define arctan $x$, as the arc between $0$ and $\pi$ which tangent is $x$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe2.htm