证明:
1/a+1/b+1/c=(ab+bc+ac)/abc
=ab+bc+ac
=(1/2)[(ab+bc)+(ab+ac)+(ac+bc)]
≥(1/2)[2(ab*bc)^(1/2)+2(ab+ac)^(1/2)+2(ac+bc)^(1/2)]
=(abc*b)^(1/2)+(abc*a)^(1/2)+(abc*c)^(1/2)
=b^(1/2)+a^(1/2)+c^(1/2)
得证.
abc=1,求证1/a+1/b+1/c大于等于根号a+根号b+根号c
abc=1,求证1/a+1/b+1/c大于等于根号a+根号b+根号c
数学人气:965 ℃时间:2020-01-27 09:28:10
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