cho `a;b;c`lớn hơn ko `a+b+c=4` `cmr:A=(a)/(b^6+729)+(b)/(c^6+729)+(c)/(a^6+729)`

Question

cho `a;b;c`lớn hơn ko
`a+b+c=4`
`cmr:A=(a)/(b^6+729)+(b)/(c^6+729)+(c)/(a^6+729)`

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Sarah 4 tuần 2021-07-11T01:06:24+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-07-11T01:08:11+00:00

    mình làm hơi tắt

    `a/(b^6+729)=1/(729)(a-a^6/(b^6+729))≥1/(729)(a-(ab^6)/(54b^3))=1/(729)(a-(ab^3)/(54))`

    tương tự `:`

    `b/(c^6+729)≥1/(729)(b-(bc^3)/(54))`

    `c/(a^6+729)≥1/(729)(c-(ca^3)/(54))`

    `⇒A≥1/(729)(a-(ab^3)/(54)+b-(bc^3)/(54)+c-(ca^3)/(54))`

    `⇒A≥1/(729)(4-(ab^3+bc^3+ca^3)/(54))` (lats mình cm ở https://hoidap247.com/cau-hoi/2031142) đây nha bạn 

    `⇒A≥1/(729)(4-(27)/(54))`

    `⇒A≥(7)/(1458)`

    `”=”`xẩy ra khi :

    `(a;b;c)=(0;1;3);(1;3;0);(3;0;1)`

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