Given-that-are-the-three-roots-of-the-equation-x-59-3-2x-64-3-3x-123-3-find-the-value-of-

Question Number 137652 by ZiYangLee last updated on 05/Apr/21

Given that α,β,γ are the three roots of the equation (x−59)^3 +(2x−64)^3 =(3x−123)^3 , find the value of α+β+γ.

$$\mathrm{Given}\:\mathrm{that}\:\alpha,\beta,\gamma\:\mathrm{are}\:\mathrm{the}\:\mathrm{three}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\left({x}−\mathrm{59}\right)^{\mathrm{3}} +\left(\mathrm{2}{x}−\mathrm{64}\right)^{\mathrm{3}} =\left(\mathrm{3}{x}−\mathrm{123}\right)^{\mathrm{3}} , \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha+\beta+\gamma. \\ $$

Answered by mitica last updated on 05/Apr/21