National and Regional Contests Turkey Contests National Olympiad First Round 2008 National Olympiad First Round 7 Turkey NMO 2008 1st Round - P07 (Algebra) Problem Statement If a = 9 3 − 3 3 + 1 a=\sqrt[3]{9}-\sqrt[3]{3}+1 a = 3 9 − 3 3 + 1 ( 4 − a a ) 6 (\frac {4-a}a)^6 ( a 4 − a ) 6 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( A ) < / s p a n > 3 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( B ) < / s p a n > 6 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( C ) < / s p a n > 8 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( D ) < / s p a n > 9 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( E ) < / s p a n > 12
<span class='latex-bold'>(A)</span>\ 3
\qquad<span class='latex-bold'>(B)</span>\ 6
\qquad<span class='latex-bold'>(C)</span>\ 8
\qquad<span class='latex-bold'>(D)</span>\ 9
\qquad<span class='latex-bold'>(E)</span>\ 12
< s p an c l a ss = ′ l a t e x − b o l d ′ > ( A ) < / s p an > 3 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( B ) < / s p an > 6 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( C ) < / s p an > 8 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( D ) < / s p an > 9 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( E ) < / s p an > 12