若把成等比数列的四个数相应的减去4,21,29,1,新的四个数成等差数列,求这四个数.
问题描述:
若把成等比数列的四个数相应的减去4,21,29,1,新的四个数成等差数列,求这四个数.
答
等比数列:a,ak,ak^2,ak^3等差数列:a-4,ak-21,ak^2-29,ak^3-1(ak^3-1) - (ak^2-29) = (ak^2-29) - (ak-21)(ak^2-29) - (ak-21) = (ak-21) - (a-4)ak^3 - 2*ak^2 + ak + 36 = 0ak^2 - 2*ak + a + 9 = 0k*(ak^2 - 2*a...