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题目设函数f(x)=2x-cosx,{an}是公差为π8的等差数列,f(a1)+f(a2)+…+f(a5)=5π,则[f(a3)]2-a1a5=().A.0B.116π2C.18π2D.1316π2此题立意高远,背景深刻,综合性强,思维量大,值得探究.本文拟从解题思路探索、问题的几何背景、问题的推广等角度,对此题进行一番研究.
The subject set the function f (x) = 2x-cosx, {an} is an arithmetic sequence with a tolerance of π8, f (a1) + f (a2) + ... + f (a5) = 5π, then [f 2-a1a5 = (). A.0B.116π2C.18π2D.1316π2 This topic is ambitious, with profound background, strong comprehensiveness and large amount of thinking. It is worth exploring. This paper attempts to explore from the problem-solving thinking, the geometric background of the problem, the problem Promotion and other aspects of this issue for some research.