已知正实数xy满足lnx+lny=0,且k(x+2y)

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已知正实数xy满足lnx+lny=0,且k(x+2y)已知正实数xy满足lnx+lny=0,且k(x+2y)已知正实数xy满足lnx+lny=0,且k(x+2y)正实数x,y满足Inx+Iny=0,∴

已知正实数xy满足lnx+lny=0,且k(x+2y)
已知正实数xy满足lnx+lny=0,且k(x+2y)

已知正实数xy满足lnx+lny=0,且k(x+2y)
正实数x,y满足Inx+Iny=0,
∴xy=1,y=1/x,
k(x+2y)≦x^2+4Y^2恒成立
∴k0,则u>=2√2,
k

lnx+lny=0
xy=1
k<=(x^2+4y^2)/(x+2y)=[(x+2y)^2-4xy]/(x+2y)
=(x+2y)-[4xy/(x+2y)]
=(x+2y)-[4/(x+2y)]
=-[-(x+2y)]+[4/-(x+2y)]
因[-(x+2y)]+[4/-(x+2y)]>=4
所以,k<=-4
k的取值范围是(-无穷,-4]