a)vì /x-2011/ là số dương =>x - 2012 là dương

=>x có nhiều giá trị

b)cũng có nhiều giá tri và làm như ý a tương tự

suy ra hai truong hop

1 : x-2011=x-2012

suy ra x-x=2011-2012(loai)

2 : x-2011=-(x-2012)

suy ra : x-2011=-x+2012                                

2x=2011+2012

2x=4023

x=2011.5

kho..................lam............................tich,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,minh..........................troi........................ret............................wa.................ung ho minh.................hu....................hu..............hu................hat..............hat....................s

a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)

\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)

\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)

\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\)    (1)

Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)

Nên biểu thức (1) xảy ra khi \(x+2013=0\)

\(x=-2013\)

b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)  (2)

Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)

Nên biểu thức (2) xảy ra khi \(x-2011=0\)

\(x=2011\)

a, Đ/k x-2012>=0 suy ra x>=2012

|x-2011|=\(\orbr{\begin{cases}x-2012\\2012-x\end{cases}}\)

TH1:x-2011=x-2012

suy ra 0=4023(loại vì mất x)

TH2: x-2011=2012-x

suy ra 2x=4023

suy ra x=2011,5

Vậy..........

k o  b i ế t  n h a

c, C=|x-1|+|x-2|+...+|x-100|=(|x-1|+|100-x|)+(|x-2|+|99-x|)+...+(|x-50|+|56-x|) \(\ge\) |x-1+100-x|+|x-2+99-x|+...+|x-50+56-x|=99+97+...+1 = 2500

Dấu "=" xảy ra khi \(\hept{\begin{cases}\left(x-1\right)\left(100-x\right)\ge0\\\left(x-2\right)\left(99-x\right)\ge0.....\\\left(x-50\right)\left(56-x\right)\ge0\end{cases}\Leftrightarrow\hept{\begin{cases}1\le x\le100\\2\le x\le99....\\50\le x\le56\end{cases}\Leftrightarrow}50\le x\le56}\)

Vậy MinC = 2500 khi 50 =< x =< 56

a. A=|x-2011|+|x-2012|=|x-2011|+|2012-x| \(\ge\) |x-2011+2012-x| = 1

Dấu "=" xảy ra khi \(\left(x-2011\right)\left(2012-x\right)\ge0\Leftrightarrow2011\le x\le2012\)

Vậy MinA = 1 khi 2011 =< x =< 2012

b, B=|x-2010|+|x-2011|+|x-2012|=(|x-2010|+|2012-x|) + |x-2011| 

Ta có: \(\left|x-2010\right|+\left|2012-x\right|\ge\left|x-2010+2012-x\right|=0\)

Mà \(\left|x-2011\right|\ge0\forall x\)

\(\Rightarrow B=\left(\left|x-2010\right|+\left|2012-x\right|\right)+\left|x-2011\right|\ge2+0=2\)

Dấu "=" xảy ra khi \(\hept{\begin{cases}\left(x-2010\right)\left(2012-x\right)\ge0\\\left|x-2011\right|=0\end{cases}\Rightarrow\hept{\begin{cases}2010\le x\le2012\\x=2011\end{cases}\Rightarrow}x=2011}\)

Vậy MinB = 2 khi x = 2011

Câu c để nghĩ