已知实数x,y,z满足X^2 y^2 z^2=5,则xy+yz+zx的最大值是 ,最小值是

题目

已知实数x,y,z满足X^2 y^2 z^2=5,则xy+yz+zx的最大值是 ,最小值是

答案

易知 2x^2+2y^2+2z^2+2xy+2yz+2zx = (x+y)^2+(y+z)^2+(z+x)^2 >=0
并且 2x^2+2y^2+2z^2-2xy-2yz-2zx = (x-y)^2+(y-z)^2+(z-x)^2 >=0
故 -5