设函数f(x)=2x-cosx,{a
n}是公差为
的等差数列,f(a
1)+f(a
2)+…+f(a
5)=5π,则[f(a
3)]
2-a
1a
5=______.
人气:159 ℃ 时间:2020-04-08 14:18:17
解答
∵f(x)=2x-cosx,
∴可令g(x)=2x+sinx,∵{a
n}是公差为
的等差数列,f(a
1)+f(a
2)+…+f(a
5)=5π
∴g(a
1-
)+g(a
2-
)+…+g(a
5-
)=0,则a
3=
,a
1=
,a
5=
∴[f(a
3)]
2-a
1a
5=π
2-
•=
,
故答案为:
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