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1987 OIM Problems/Problem 5

Revision as of 12:54, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == If <math>r</math>, <math>s</math>, and <math>t</math> are all the roots of the equation: <cmath>x(x-2)3x-7)=2</cmath> (a) Prove that <math>r</math>, <math>s</ma...")
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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 $x$.



Solution

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