Cho `1≥a,b,c ≥0` `CMR: a+b^2+c^3-ab-bc-ca≤1`

Question

Cho `1≥a,b,c ≥0`
`CMR: a+b^2+c^3-ab-bc-ca≤1`

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Acacia 9 months 2021-04-23T21:10:27+00:00 2 Answers 13 views 0

Answers ( )

  1. ngockhue
    0
    2021-04-23T21:11:41+00:00
    Reply

    Do `1≥a,b,c≥0` nên :

    `(1-a)(1-b)(1-c)≥0`

    `⇒` `1-a-b-c+ab+ac+cb-abc≥0`

    `⇒` `a+b+c-ab-ac-cb≤1-abc≤1`

    Chú ý :  Do `1≥b,c≥0` nên : `b^2≤b` `;` `c^3≤c`. Suy ra :

    `a+b^2+c^3-ab-bc-ca≤a+b+c-ab-ac-cb≤1-abc≤1`    `⇒` `đpcm`

     

  2. Neala
    0
    2021-04-23T21:12:22+00:00
    Reply

    xin hay nhất cho nhóm ạ 

    cho-1-a-b-c-0-cmr-a-b-2-c-3-ab-bc-ca-1

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