X>0 Y>0证1/x+1/y>=4/(x+y)X>0 Y>0 证1/x+1/y>=4/(x+y)
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X>0 Y>0证1/x+1/y>=4/(x+y)X>0 Y>0 证1/x+1/y>=4/(x+y)
X>0 Y>0证1/x+1/y>=4/(x+y)
X>0 Y>0
证1/x+1/y>=4/(x+y)
X>0 Y>0证1/x+1/y>=4/(x+y)X>0 Y>0 证1/x+1/y>=4/(x+y)
本题实际考察均值不等式的运用
解法如下
因为 xy=(x+y)/{(x+y)/2}^2
即有 1/x+1/y>=4/(x+y)
X>0 Y>0证1/x+1/y>=4/(x+y)X>0 Y>0 证1/x+1/y>=4/(x+y)
x>0 y>0 x+y=1 证(x+1/x)(y+1/y)≥25/4
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