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数学
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若a,b,c成G.P,m和n分别是a,b及b,c的等比中项,则(a/m)+(c/n)的值?
但是,
人气:278 ℃ 时间:2020-05-25 11:23:24
解答
b^2=ac
m^2=ab推出a/m=m/b
n^2=bc推出c/n=n/b
(a/m)+(c/n)的值即为(m+n)/b,再将之平方,
(m+n)^2/b^2=(a+c+2b)/b
故(a/m)+(c/n)=根号下(a+c+2b)/b
若abc是已知数的话.
那最小值为2呀,a=c=b时取等(运用均值不等式)
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