cauchy inequalities.ppt

7/24/2019 cauchy inequalities.ppt

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!"#$%

& '()

!"# $%*+,-./ 0 '()

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12 45 1343567"


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[ +89: ]

(a1b1 ; a2b2)2

2 /?@ ABC5'=>

D |||||| EFGHIJH5'=>K= LMNLO7PQ


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2


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4. S) x,y TU xy>0, I x2y=4, X xy+x2 !# .

3

33

2

2 2 2

2

2

2

2

2

23

4

4 4

2 2

: xy 0, x y 4,

y 0, x 0.

xy x x x

2 23 4.

22 3

x

x 3

x 4., x , xy x

x

x x

x

x x x x

x

= +

> =

= > >

+ = + = +

+

=

= +

=

Q

HIJHY7Z[!#


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6 x,y,z

2x+2y+z=1, 1 3xy+yz+xz

2011

xz

1

zy

1

yx

1)3(


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cauchy inequalities.ppt