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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Melanie 4 tuần 2021-09-06T10:25:33+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-09-06T10:26:42+00:00

    xin hay nhất cho nhóm ạ 

    0
    2021-09-06T10:27:15+00:00

    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`

     

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