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Algebra Difficulty 4.6 AIME Prove it Soviet Union
Problem:
Show that {x}4>{x}−1/2 for all real x.
Solution
Solution:
{x}4−{x}+1/2=({x}2−1/2)2+({x}−1/2)2≥0. We could only have equality if {x}2={x}=1/2, which is impossible, so the inequality is strict.
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