Tìm GTNN của : (trog ảnh)

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Tìm GTNN của :
(trog ảnh)
tim-gtnn-cua-trog-anh

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Thiên Hương 4 years 2021-05-18T20:23:01+00:00 2 Answers 14 views 0

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  1. bonexptip
    0
    2021-05-18T20:24:34+00:00
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    Đáp án:

     Đặt `A = 4x^2 – 4x – 3|2x – 1| + 3`

    Ta có : 

    `A = (4x^2 – 4x + 1) – 3|2x – 1| + 2`

    `= (2x – 1)^2 – 3|2x – 1| + 2`

    `= |2x – 1|^2 – 3|2x – 1| + 2`

    `= |2x – 1|^2 – 2 . |2x – 1| . 3/2 + 9/4 – 1/4`

    `= (|2x – 1| – 3/2)^2 – 1/4 >= -1/4`

    Dấu “=” xảy ra `<=> |2x – 1| – 3/2 = 0 <=> |2x – 1| = 3/2`

    `<=> ` \(\left[ \begin{array}{l}2x – 1 =\dfrac{3}{2} \\2x – 1 = \dfrac{-3}{2}\end{array} \right.\) 

    `<=> ` \(\left[ \begin{array}{l}x=\dfrac{5}{4}\\x=\dfrac{-1}{4}\end{array} \right.\)

    Vậy `GTNN` của `A` là `-1/4 <=>` \(\left[ \begin{array}{l}x=\dfrac{5}{4}\\x=\dfrac{-1}{4}\end{array} \right.\)

    Giải thích các bước giải:

     

  2. Nho
    0
    2021-05-18T20:24:55+00:00
    Reply

    `4x^2-4x-3|2x-1|+3`

    `=4x^2-4x-3|2x-1|+1+2`

    `=4x^2-4x+1-3|2x-1|+2`

    `=(4x^2-4x+1)-3|2x-1|+2`

    `=[(2x)^2-2.2x+1^2]-3|2x-1|+2`

    `=(2x-1)^2-3|2x-1|+2`

    `=|2x-1|^2-3|2x-1|+2`

    `=|2x-1|^2-2|2x-1|3/2+(3/2)^2-1/4`

    `=(|2x-1|-3/2)^2-1/4`

    Do `(|2x-1|-3/2)^2≥0`

    `⇒(|2x-1|-3/2)^2-1/4≥-1/4`

    Dấu “=” xảy ra khi `(|2x-1|-3/2)^2=0`

    `⇔|2x-1|-3/2=0`

    `⇔|2x-1|=3/2`

    `⇔` \(\left[ \begin{array}{l}2x-1=\dfrac{3}{2}\\2x-1=-\dfrac{3}{2}\end{array} \right.\) 

    `⇔` \(\left[ \begin{array}{l}2x=\dfrac{5}{2}\\2x=-\dfrac{1}{2}\end{array} \right.\) 

    `⇔` \(\left[ \begin{array}{l}x=\dfrac{5}{4}\\x=-\dfrac{1}{4}\end{array} \right.\) 

    Vậy GTNN của phương trình `4x^2-4x-3|2x-1|+3=-1/4` khi `x=5/4` hoặc `x=-1/4`

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )