Tinh GTLN -3x *(x+3)-7

Question

Tinh GTLN
-3x *(x+3)-7

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Sapo 8 tháng 2020-10-15T00:54:19+00:00 2 Answers 87 views 0

Answers ( )

  1. `-3x(x+3)-7`

    `=-3x^2-9x-7`

    `=-3(x^2+3x+7/3)`

    `=-3[(x^2+2.x.3/2+3/4)+19/12]`

    `=-3[(x+3/2)^2+19/12]`

    `=-19/4-3(x+3/2)^2≤-19/4` (Vì `(x+3/2)^2≥0∀x`)

    Dấu ”=” xảy ra ⇔`(x+3/2)^2=0⇔x=-3/2`

    Vậy GTLN của bt là -19/4 ⇔x=-3/2

     

  2. `-3x(x+3)-7=-3x^2-9x-7`

    `=-3(x^2+3x+7/3)`

    `=-3.[(x^2+2 . x . 3/2+3/4)+19/12]`

    `=-3.[(x+3/2)^2+19/12]`

    `=-19/4-3(x+3/2)^2` $\leq$ `-19/4` (Vì `(x+3/2)^2` $\geq$ `0`)

    $Dấu$ `=` $xảy$ $ra$ ⇔`(x+3/2)^2=0⇔x=-3/2`

    $Vậy$ ….

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