tìm max y, min y

V

vanninza

vì an fa trong khỏng (0 ;pi/2)
nên sin trong khoản (0 ;1)
cos trong khoản ( 0 :1)
=> sin^2 >hoặc= sin^20
cos^2>hặc=cos^20
sin^20 +cos^20<hoặc=sin^2+cos^2 =1
vậy max =1
 
C

conga222222

$\eqalign{
& \cos i: \cr
& {\sin ^{20}}x + \underbrace {{1 \over {1024}} + ... + {1 \over {1024}}}_{9\;so} \ge 10\root {10} \of {{{{{\sin }^{20}}x} \over {{{1024}^9}}}} = {{5{{\sin }^2}x} \over {256}} \cr
& \to {\sin ^{20}}x \ge {{5{{\sin }^2}x} \over {256}} - {9 \over {1024}} \cr
& tuong\;tu \cr
& {\cos ^{20}}x \ge {{5{{\cos }^2}x} \over {256}} - {9 \over {1024}} \cr
& \to {\sin ^{20}}x + {\cos ^{20}}x \ge {{5\left( {{{\sin }^2}x + {{\cos }^2}x} \right)} \over {256}} - {{18} \over {1024}} = {1 \over {512}} \cr
& dau = \leftrightarrow \sin x = \cos x = {{\sqrt 2 } \over 2} \cr} $
 
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