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P24 [Algebra] - Turkish NMO 1st Round - 2003

Source:

May 18, 2014
algebrapolynomial

Problem Statement

If 3a=1+23a=1+\sqrt 2, what is the largest integer not exceeding 9a4−6a3+8a2−6a+99a^4-6a^3+8a^2-6a+9?
<spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 9 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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