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>0Y>0证1/x+1/y>=4/(x+y)X>0Y>0证1/x+1/y>=4/(x+y)X>0Y>0证1/x+1/y>=4/(x+y)X>0Y>0证1/x+1/y>=4/(x+y)X>0Y>0证1
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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{x+y=1 ,xy=-6{x(2x-3)=0,y=x²-1{(3x+4y-3)(3x+4y+3)=0,3x+2y=5{(x-y+2)(x+y)=0,x²+y²=8{(x+y)((x+y-1)=0,(x-y)(x-y-1)=0
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