Tham khảo:

CHÚC EM HỌC TỐT NHÁ

\(\left|x-2017\right|+\left|x-2008\right|\)

\(=\left|x-2007\right|+\left|x-2008\right|\ge\left|x-2007+2008-x\right|=1\)

Dấu "=" sảy ra:

\(\Leftrightarrow\left(x-2007\right)\left(2008-x\right)\ge0\)

\(\Leftrightarrow2007\le x\le2008\)

mk ko viết lại đề đâu nha làm luôn đấy

M=|3-x|+|x-7|+|x+2018|

\(\le\left|3-x+x+2018\right|+\)\(\left|x-7\right|\)

=|2021|+|x-7|

Dấu "=" xảy ra khi (3-x)(x+2018)\(\ge0\)

\(\Leftrightarrow\hept{\begin{cases}3-x\ge0\\x+2018\ge0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ge3\\x\le2018\end{cases}\Rightarrow3\le x\le2018}\)

Do |x-7|\(\ge0\) nên GTNN của M=2021 khi và chỉ khi x-7=0 => x=7(t/m \(3\le x\le2018\))

vậy GTNN của M=2021 khi x=7

tk cho mk nha bn 

***** Chúc bạn học giỏi*****

Mik cũng làm được kết quả như bạn!! Hihi. Dù sao cũng cảm ơn bạn nhiều nha... 

hi sư huynh đệ mới lớp 6

\(A=\frac{x^2-2x+2007}{2007x^2},\left(x\ne0\right)\)

\(A=\frac{2007x^2-2x.2007+2007^2}{2007x^2}=\frac{x^2-2x.2007+2007^2}{2007x^2}+\frac{2006x^2}{2007x^2}=\) \(\frac{\left(x-2007\right)^2}{2007x^2}+\frac{2006}{2007}\ge\frac{2006}{2007}\)

\(A_{min}=\frac{2006}{2007}\) khi \(x-2007=0\) hay \(x=2007\)

Chúc bạn học tốt !!!

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12007" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">12007 - 22007x" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">22007x + 1x2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">1x2

1x2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">1x2 - 22007x" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">22007x + 120072" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">120072 ) + (12007−120072" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">12007−120072 )

1x−12007" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">1x−12007)12007−120072" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">12007−120072)

1x−12007" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">1x−12007 = 0

<=> x = 2007

Vậy x = 2007 thì Amin

bài này từng có trên violimpic đấy bạn

dễ ợt 2008

giải đi chứ

Ta có |x-2006| \(\ge\) 0 với mọi x

         (x-y+1)^2 \(\ge\)0 với mọi x;y

=>|x-2006|+(x-y+1)^2+2008 \(\ge\) 2008 với mọi x;y

Dấu "=" sảy ra khi x-2006=0 => x=2006

                           x-y+1=0 =>2006-y+1=0 => 2006-y=-1 => y=2006+1=2007

Vậy Min M=2008 tại x=2006 và y=2007

thk bạn