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Turkish NMO First Round - 2012 Problem - 23 {Algebra}

Source:

July 1, 2012
algebrapolynomialVieta

Problem Statement

a,b,ca,b,c are distinct real roots of x33x+1=0x^3-3x+1=0. a8+b8+c8a^8+b^8+c^8 is
<spanclass=latexbold>(A)</span> 156<spanclass=latexbold>(B)</span> 171<spanclass=latexbold>(C)</span> 180<spanclass=latexbold>(D)</span> 186<spanclass=latexbold>(E)</span> 201 <span class='latex-bold'>(A)</span>\ 156 \qquad <span class='latex-bold'>(B)</span>\ 171 \qquad <span class='latex-bold'>(C)</span>\ 180 \qquad <span class='latex-bold'>(D)</span>\ 186 \qquad <span class='latex-bold'>(E)</span>\ 201