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Regional Olympiad - FBH 2011 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 26, 2018
algebrapolynomial

Problem Statement

Find the real number coefficient cc of polynomial x2+x+cx^2+x+c, if his roots x1x_1 and x2x_2 satisfy following: 2x132+x2+2x232+x1=−1\frac{2x_1^3}{2+x_2}+\frac{2x_2^3}{2+x_1}=-1
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