求函数y=x^2/x-2(x>2)的最小值

问题描述:

求函数y=x^2/x-2(x>2)的最小值
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y=x²/(x-2)=(x²-4+4)/(x-2)=[(x+2)(x-2)+4]/(x-2)=x+2 +4/(x-2)=(x-2) +4/(x-2) +4x-2>0 4/(x-2)>0由均值不等式得:当x-2=4/(x-2)时,即x=4时,(x-2)+ 4/(x-2)有最小值4此时(x-2)+ 4/(x-2) +4有最小值4+4=8y...