3个正数a,b,c成等比数列,则lga,lgb,lgc是?

2025-04-04 23:04:40
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回答1:

lga lgb lgc = 3,即 lgabc = 3,则abc = 10^3
又三个正数abc成等比数列,设ac = b^2,所以,b^3 = 10^3, 则 b = 10
设公比 q,由a b c = 62,得
10/q 10 10q = 62,即5q^2 -26q 5 =0
解得,q = 1/5 或 q = 5
所以,这三个正数是 2,10,50