Difference between revisions of "1987 OIM Problems/Problem 5"
(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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Note: We define arctan <math>x</math>, as the arc between <math>0</math> and <math>\pi</math> which tangent is <math>x</math>. | Note: We define arctan <math>x</math>, as the arc between <math>0</math> and <math>\pi</math> which tangent is <math>x</math>. | ||
| − | + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | |
| − | |||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe2.htm | ||
Latest revision as of 12:27, 13 December 2023
Problem
If 
, 
, and 
are all the roots of the equation:
![\[x(x-2)3x-7)=2\]](http://latex.artofproblemsolving.com/1/7/2/1725d618bea9139962705cbb901973e42fbe129d.png)
(a) Prove that , , and are all postive
(b) Calculate: arctan + arctan + arctan .
Note: We define arctan 
, as the arc between 
and 
which tangent is .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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