一道简单的不等式题目~
详细的解答过程哦~
x^2/(x-1)=[(x-1)^2+2(x-1)+1]/(x-1) =(x-1)+2+1/(x-1) =[(x-1)+1/(x-1)]+2 因为x>1--->x-1>0,由均值不等式,有 (x-1)+1/(x-1)>=2.当仅当x-1=1/(x-1)--->(x-1)^2=1--->x=2(已舍去x=0)时等号成立。 --->(x-1)+1/(x-1)+2>=4. 所以x=2时x^2/(x-1)有最小值4.
答:依排序不等式易知:1/bc≥1/ca≥1/ab, ∴a^5/(bc)^3+b^5/(ca)^3+c^5/(ab)^3 ≥b^5/(bc)^3+c^5/(ca)^...详情>>
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