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在现行高中数学教材(人教版)及学前教育专业数学教材(复旦大学出版社)中,对于定理:如果a>0,b>0,那么a+b/2≥(ab)~(1/2)(当且仅当a=b时取“=”号)的几何意义解释如下:以a+b长的线段为直径作圆,在直径AB上取点C,使AC=a,CB=b.过点C作垂直于直径AB的弦DD′,连结AD、DB,易证RtΔACD～RtΔDCB,那么CD~((2))=CA·CB,即CD=(ab)~(1/2).
In the current high school mathematics textbook (PEP) and preschool math textbook (Fudan University Press), for the theorem: if a> 0, b> 0 then a + b / 2≥ (ab) 2) (if and only if a = b, the meaning of “= ”) is explained as follows: Take a line with a + b as the diameter for a circle, take a point C on the diameter AB to make AC = a, CB = b. If point C crosses the chord DD 'perpendicular to the diameter AB and connects AD, DB, then it is easy to prove RtΔACD ~ RtΔDCB that CD = (abc) ~ CA · CB /2).