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22 tháng 10 2018

\(\left|x+\dfrac{1}{101}\right|+\left|x+\dfrac{2}{101}\right|+\left|x+\dfrac{3}{101}\right|+...+\left|x+\dfrac{100}{101}\right|=101x\)

Ta có : \(\left\{{}\begin{matrix}\left|x+\dfrac{1}{101}\right|\ge0\\\left|x+\dfrac{1}{102}\right|\ge0\\....\\\left|x+\dfrac{100}{101}\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{1}{101}\right|+\left|x+\dfrac{2}{101}\right|+\left|x+\dfrac{3}{101}\right|+...+\left|x+\dfrac{100}{101}\right|\ge0\)

\(\Rightarrow101x\ge0\)

\(\Rightarrow x\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{1}{101}\right|=x+\dfrac{1}{101}\\\left|x+\dfrac{2}{101}\right|=x+\dfrac{2}{101}\\....\\\left|x+\dfrac{100}{101}\right|=x+\dfrac{100}{101}\end{matrix}\right.\)

\(\Rightarrow x+\dfrac{1}{101}+x+\dfrac{2}{101}+x+\dfrac{3}{101}+...+x+\dfrac{100}{101}=101x\)

\(\Rightarrow100x+\dfrac{1+2+3+...+100}{101}=101x\)

\(\Rightarrow100x+\dfrac{5050}{101}=101x\)

\(\Rightarrow100x+50=101x\)

\(\Rightarrow101x-100x=50\)

\(\Rightarrow x=50\)

Vậy \(x=50\)

26 tháng 9 2017

\(\left|x+\dfrac{1}{101}\right|+\left|x+\dfrac{2}{101}\right|+.....+\left|x+\dfrac{100}{101}\right|=101x\left(1\right)\)

VT(1) \(\ge0\) \(\Rightarrow VP\left(1\right)\ge0\Rightarrow101x\ge0\Rightarrow x\ge0\)

\(\Rightarrow\left|x+\dfrac{1}{101}\right|+\left|x+\dfrac{2}{101}\right|+...+\left|x+\dfrac{100}{101}\right|=100x+\dfrac{5050}{101}=101x\\ \Rightarrow x=50\)

24 tháng 9 2017

tim gtln

22 tháng 10 2018

Vì \(\left|x+\frac{1}{101}\right|\ge0;\left|x+\frac{2}{101}\right|\ge0;...;\left|x+\frac{100}{101}\right|\ge0\forall x\)

\(\Rightarrow\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+...+\left|x+\frac{100}{101}\right|\ge0\forall x\)

\(\Rightarrow101x\ge0\)

\(\Rightarrow x\ge0\)

Từ điều kiện trên ta có :

\(x+\frac{1}{101}+x+\frac{2}{101}+...+x+\frac{100}{101}=101x\)

\(100x+\frac{1+2+...+100}{101}=101x\)

\(101x-100x=\frac{5050}{101}\)

\(x=50\)

Vậy x = 50

22 tháng 10 2018

\(\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+....+\left|x+\frac{100}{101}\right|=101x\)

\(KĐ:101x\ge0\Rightarrow x\ge0\)

\(\Rightarrow\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+...+\left|x+\frac{100}{101}\right|=101x\)

\(x+\frac{1}{101}+x+\frac{2}{101}+....+x+\frac{100}{101}=101x\)

\(100x+\left(\frac{1}{101}+\frac{2}{101}+....+\frac{100}{101}\right)=101x\)

\(\Rightarrow101-100x=\frac{1+2+....+100}{101}\)

\(x=\frac{\left(1+100\right)\left(100-1+1\right):2}{101}\)

\(x=\frac{101.100:2}{101}\)

\(x=50\)

17 tháng 2 2017

Ta có: \(\left|x+\frac{1}{101}\right|\ge0\); \(\left|x+\frac{2}{101}\right|\) \(\ge0\); ...; \(\left|x+\frac{100}{101}\right|\ge0\)

\(\Rightarrow101x\ge0\)

\(\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+...+\left|x+\frac{100}{101}\right|\ge0\)

\(\Rightarrow\left|x+\frac{1}{101}\right|=x+\frac{1}{101}\); \(\left|x+\frac{2}{101}\right|=x+\frac{2}{101}\); ...; \(\left|x+\frac{100}{101}\right|=x+\frac{100}{101}\)

Thay vào đề bài ta đc:

\(x+\frac{1}{101}+x+\frac{2}{101}+...+x+\frac{100}{101}=101x\)

\(\Rightarrow\left(x+x+...+x\right)+\left(\frac{1}{101}+\frac{2}{101}+...+\frac{100}{101}\right)=101x\)

\(\Rightarrow\) \(100x\) + \(\left(\frac{1+2+...+101}{101}\right)=101x\)

\(\Rightarrow100x+101=101x\)

\(\Rightarrow x=101\)

Vậy \(x=101.\)

17 tháng 2 2017

\(\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+\left|x+\frac{3}{101}\right|+....+\left|x+\frac{100}{101}\right|\)=101x (1)

điều kiện:101x\(\ge\) 0 \(\Rightarrow\) x\(\ge\) 0

từ (1) \(\Rightarrow\) \(x+\frac{1}{101}+x+\frac{2}{101}+...+x+\frac{100}{101}\)=101x

\(\Rightarrow\) 100x+(\(\frac{1}{101}+\frac{2}{101}+...+\frac{100}{101}\))=101x

\(\Rightarrow\) 100x+\(\frac{5050}{101}\)=101x

\(\Rightarrow\) \(\frac{5050}{101}\)=101x-100x

\(\Rightarrow\) x=50

k bt mk lm sai hay lm đúng nữa

nếu mk lm sai thì thôi nha!

13 tháng 9 2016

Vì \(\left|x+\frac{1}{101}\right|+\left|x+\frac{1}{102}\right|+....+\left|x+\frac{100}{101}\right|>0\)

\(\Rightarrow101x>0\)

\(\Rightarrow x>0\)

\(\Rightarrow\left(x+\frac{1}{101}\right)+.....+\left(x+\frac{100}{101}\right)=101x\)

\(\Rightarrow100x+\left(\frac{1}{101}+\frac{2}{101}+....+\frac{100}{101}\right)=101x\)

\(\Rightarrow x=\frac{\left(100+1\right)100:2}{101}\)

\(\Rightarrow x=\frac{50.101}{101}\)

\(\Rightarrow x=50\)

Vậy x = 50

13 tháng 9 2016

Do \(\left|x+\frac{1}{101}\right|\ge0;\left|x+\frac{2}{101}\right|\ge0;\left|x+\frac{3}{101}\right|\ge0;...;\left|x+\frac{100}{101}\right|\ge0\)

=> \(101x\ge0\)

=> \(x\ge0\)

=> \(\left(x+\frac{1}{101}\right)+\left(x+\frac{2}{101}\right)+\left(x+\frac{3}{101}\right)+...+\left(x+\frac{100}{101}\right)=101x\)

=> \(\left(x+x+x+...+x\right)+\left(\frac{1}{101}+\frac{2}{101}+\frac{3}{101}+...+\frac{100}{101}\right)=101x\)

            100 số x                          100 phân số

=> \(100x+\frac{\left(1+100\right).100:2}{101}=101x\)

=> \(\frac{101.50}{101}=101x-100x\)

=> \(x=50\)

11 tháng 10 2018

Do \(\left|a\right|\ge0\) nên:

a) \(\left|x+\frac{1}{101}\right|+\left|x+\frac{2}{101}\right|+...+\left|x+\frac{100}{101}\right|=101x\ge0\)

\(\Rightarrow\left(x+x+...+x\right)+\left(\frac{1}{101}+\frac{2}{101}+...+\frac{100}{101}\right)=101x\) (100 số hạng x)

\(\Leftrightarrow100x+5050=101x\Leftrightarrow201x=5050\Leftrightarrow x=\frac{5050}{201}\)

b) Đề sai nhé!

11 tháng 10 2018

Chết,nhầm ở câu cuối cùng của câu a) . Mình là ẩu thật :v. Sửa lại nhé:

\(\Leftrightarrow100x+\frac{5050}{101}=101x\Leftrightarrow100x+50=101x\Leftrightarrow201x=50\Leftrightarrow x=\frac{50}{201}\)

19 tháng 9 2016

a ) \(3-4.\left|5-6x\right|=7\)

\(\Leftrightarrow4.\left|5-6x\right|=-4\)

\(\Leftrightarrow\left|5-6x\right|=-1\)

\(\Leftrightarrow\) Không thõa mãn ( vì \(x\ge0\) )

19 tháng 9 2016

b) Do \(\left|x+2\right|\ge0;\left|x+\frac{3}{5}\right|\ge0;\left|x+\frac{1}{2}\right|\ge0\)

=> \(4x\ge0\)

=> \(x\ge0\)

Lúc này ta có: \(\left(x+2\right)+\left(x+\frac{3}{5}\right)+\left(x+\frac{1}{2}\right)=4x\)

=> \(\left(x+x+x\right)+\left(2+\frac{3}{5}+\frac{1}{2}\right)=4x\)

=> \(3x+\frac{31}{10}=4x\)

=> \(4x-3x=\frac{31}{10}\)

=> \(x=\frac{31}{10}\)

Vậy \(x=\frac{31}{10}\)

c) Do \(\left|x+\frac{1}{101}\right|\ge0;\left|x+\frac{2}{101}\right|\ge0;\left|x+\frac{3}{101}\right|\ge0;...;\left|x+\frac{100}{101}\right|\ge0\)

=> \(101x\ge0\)

=> \(x\ge0\)

Lúc này ta có: \(\left(x+\frac{1}{101}\right)+\left(x+\frac{2}{101}\right)+\left(x+\frac{3}{101}\right)+...+\left(x+\frac{100}{101}\right)=101x\)

=> \(\left(x+x+x+...+x\right)+\left(\frac{1}{101}+\frac{2}{101}+\frac{3}{101}+...+\frac{100}{101}\right)=101x\)

               100 số x

=> \(100x+\frac{\left(1+100\right).100:2}{101}=101x\)

=> \(\frac{101.50}{101}=101x-100x\)

=> \(x=50\)

Vậy x = 50

4 tháng 8 2019

Ta có: 

\(F\left(100\right)=100^{10}-101.100^9+101.100^8-101.100^7+...-101.100+101\)

       \(=100-\left(100+1\right).100^9+\left(100+1\right).100^8-\left(100+1\right).100^7+...-\left(100+1\right).100+101\)

 \(=100^{10}-100^{10}-100^9+100^9+100^8-100^8-100^7+...-100^2-100+101\)

\(=1\)

Ta có:\(101=100+1=x+1\)

\(\Rightarrow F\left(100\right)=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-...-\left(x+1\right)x+x+1\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-...-x^2-x+x+1=1\)