如题:设a>b>0,则a²+[1/(a*b)] +[1/(a*(a-b))]的最小值是?( D A.1 B.2 C.3 D.4PS:老师今天没来上课,这题是试卷上的,我做了很久做不出来,看了答案解释也不太明白(特别是“a²+[1/(a*b)] +[1/(a
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![如题:设a>b>0,则a²+[1/(a*b)] +[1/(a*(a-b))]的最小值是?( D A.1 B.2 C.3 D.4PS:老师今天没来上课,这题是试卷上的,我做了很久做不出来,看了答案解释也不太明白(特别是“a²+[1/(a*b)] +[1/(a](/uploads/image/z/6984394-34-4.jpg?t=%E5%A6%82%E9%A2%98%EF%BC%9A%E8%AE%BEa%EF%BC%9Eb%EF%BC%9E0%2C%E5%88%99a%26%23178%3B%2B%5B1%2F%EF%BC%88a%2Ab%29%5D+%2B%5B1%2F%28a%2A%28a-b%29%29%5D%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E6%98%AF%3F%EF%BC%88+D+A.1+B.2+C.3+D.4PS%EF%BC%9A%E8%80%81%E5%B8%88%E4%BB%8A%E5%A4%A9%E6%B2%A1%E6%9D%A5%E4%B8%8A%E8%AF%BE%2C%E8%BF%99%E9%A2%98%E6%98%AF%E8%AF%95%E5%8D%B7%E4%B8%8A%E7%9A%84%2C%E6%88%91%E5%81%9A%E4%BA%86%E5%BE%88%E4%B9%85%E5%81%9A%E4%B8%8D%E5%87%BA%E6%9D%A5%2C%E7%9C%8B%E4%BA%86%E7%AD%94%E6%A1%88%E8%A7%A3%E9%87%8A%E4%B9%9F%E4%B8%8D%E5%A4%AA%E6%98%8E%E7%99%BD%EF%BC%88%E7%89%B9%E5%88%AB%E6%98%AF%E2%80%9Ca%26%23178%3B%2B%5B1%2F%EF%BC%88a%2Ab%29%5D+%2B%5B1%2F%28a)
如题:设a>b>0,则a²+[1/(a*b)] +[1/(a*(a-b))]的最小值是?( D A.1 B.2 C.3 D.4PS:老师今天没来上课,这题是试卷上的,我做了很久做不出来,看了答案解释也不太明白(特别是“a²+[1/(a*b)] +[1/(a
如题:设a>b>0,则a²+[1/(a*b)] +[1/(a*(a-b))]的最小值是?( D
A.1 B.2 C.3 D.4
PS:老师今天没来上课,这题是试卷上的,我做了很久做不出来,看了答案解释也不太明白(特别是“a²+[1/(a*b)] +[1/(a*(a-b))]=a²+1/[b*(a-b)]≥a²+(4/a²)≥4”这部分,不知是怎样配凑而来的,碰到要配凑的就不会了,不懂配凑),跟同学讨论了,没多大结果(╯▽╰)希望数详细学达人能够再详细地帮忙解说一下其解题过程,根据回答的具体程度,50,辛苦了!
a²+[1/(a*b)] +[1/(a*(a-b))]=a²+1/[b*(a-b)]≥a²+(4/a²)≥4,当且仅当b=a-b
且a²=4/a²,即a=√2,b=√2/2时,“=”都成立,故原式的最小值为4,选D.
如题:设a>b>0,则a²+[1/(a*b)] +[1/(a*(a-b))]的最小值是?( D A.1 B.2 C.3 D.4PS:老师今天没来上课,这题是试卷上的,我做了很久做不出来,看了答案解释也不太明白(特别是“a²+[1/(a*b)] +[1/(a
[1/(a*b)] +[1/(a*(a-b))] = 1/[b*(a-b)] 通分,就能求得 这部分简单的
有这么一条公式(a-b)²>=0 所以 (a+b)²>=4ab 所以 ab=2*a*(2/a)=4