Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1987 OIM Problems/Problem 5

Revision as of 11:54, 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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1987_OIM_Problems/Problem_5&oldid=206979"