实数a.b.c满足x+y+z=5,xy+yz+zx=3,求z的最大值
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实数a.b.c满足x+y+z=5,xy+yz+zx=3,求z的最大值
x+y=5-z,(x+y)²=(5-z)²,(x+y)²/4>=xy,(5-z)² /4>=xy
xy+yz+zx=3, xy=3-z(x+y)=3-z(5-z)
(5-z)² /4>=3-z(5-z)
3z²-10z-13<=0
-1<=z<=13/3
z的最大值为13/3
xy+yz+zx=3, xy=3-z(x+y)=3-z(5-z)
(5-z)² /4>=3-z(5-z)
3z²-10z-13<=0
-1<=z<=13/3
z的最大值为13/3
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