Current location - Training Enrollment Network - Mathematics courses - 20 12 solving math problems in Sichuan liberal arts in college entrance examination
20 12 solving math problems in Sichuan liberal arts in college entrance examination
20 12 solving math problems in Sichuan liberal arts in college entrance examination

Let the function f (x) = (x-3) 3+x- 1, {an} is a arithmetic progression with a tolerance other than 0, f (a1)+f (a2)+...+f () a7 =14, and then a.

Analysis: ∫{ an} is a arithmetic progression with a tolerance of not 0, f (a1)+f (a2)+...+f () a7 =14.

∴[(a 1-3)^3+a 1- 1]+[(a2-3)^3+a2- 1]+…+[(a7-3)^3+a7- 1]= 14

∵ The function h (x) = x 3 is a odd function, which is symmetric about the origin center.

∴ h (x-3) = (x-3) 3, which is symmetric about the center of point (3,0).

∫{ an} is an arithmetic series, and the tolerance is not 0.

∴h(a 1)+h(a2)+.....+h(a7)=0

∴ points (A 1, H (A 1)), (A2, H (A2)), ... and (A7, H (A7)), (A6, H (A6)), ...

(a4,h(a4)=(3,0)

∴(a 1-3)^3+[(a2-3)^3+…+[(a7-3)^3=0

∴[(a 1-3)^3+a 1- 1]+[(a2-3)^3+a2- 1]+…+[(a7-3)^3+a7- 1]= 14

a 1- 1+a2- 1+…+a7- 1 = 14

a 1+a2+…a7 = 7+ 14 = 2 1