Roots and Arctangents

Problem

Let x1,x2,x3x_1, x_2, x_3 be the roots of x3−17x−18=0x^3 - 17x - 18 = 0, with −4<x1<−3-4 < x_1 < -3 and 4<x3<54 < x_3 < 5.

1. Find the integer part of x2x_2. 2. Evaluate arctan⁡x1+arctan⁡x2+arctan⁡x3\arctan x_1 + \arctan x_2 + \arctan x_3.

Answer

Solution

Difficulty7/10
Topicstrigonometry, algebra, Trigonometric Identities, Estimation, Vieta's Formulas

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