2012 + 2013 x 2014 / 2014 x 2015 -2016 = 1 

mình trả lời đầu tiên nha

bn giải tri tiết giùm mình được không

2013 x 2014 +2012 / 2015 x2015 -2016=4054182+2012 / 4058210 - 2016= 4056194/4056194=1

\(\frac{2012+2013.2014}{2014.2015-2016}\)= \(\frac{2012+2013.2014}{2014.\left(2013+2\right)-2016}\) = \(\frac{2012+2013.2014}{2014.2013+2.2014-2016}\)= \(\frac{2012+2013.2014}{2014.2013+4028-2016}\)= \(\frac{2012+2013.2014}{2014.2013+2012}\)= \(1\)

2012 +2013 X 2014/2014X2015-2016=???????????//?????/

Áp dụng bđt |a|+|b|+|c|+|d| \(\ge\)|a+b+c+d| ta có:

B = |x-2016|+|x-2015|+|x-2014|+|x-2013|+|x-2012|+2016

B = |2016-x|+|2015-x|+|x-2014|+|x-2013|+|x-2012|+2016 \(\ge\) |(2016-x)+(2015-x)+0+(x-2013)+(x-2012)|+2016 = |6|+2016 = 6+2016 = 2022

Dấu "=" xảy ra khi \(\left\{\begin{matrix}x-2015\le0\\x-2014=0\\x-2013\ge0\end{matrix}\right.\) => x = 2014

Ta có: \(\left|x-2016\right|\ge0\forall x\in R\)

\(\left|x-2015\right|\)\(\ge0\forall x\in R\)

.....................

=> |x-2016|+|x-2015|+|x-2014|+|x-2013|+|x-2012| \(\ge0\forall x\in R\)

=> |x-2016|+|x-2015|+|x-2014|+|x-2013|+|x-2012| + 2016 \(\ge0\forall x\in R\)

4056191

4056191

tích mình đi mà

4056191 bạn nhé chúc bạn học tốt

\(\frac{2012+2013.2014}{2014.2015-2016}\)

\(\frac{2012+2013.2014}{2014.\left(2013+2\right)-2016}\)

\(\frac{2012+2013.2014}{2014.2013+2014.2-2016}\)

\(\frac{2012}{2012}\)

\(1\)

2012+2013x2014/2014x2015-2016

=2012+4054182/4058210-2016

=4056194:4056194

=1

( 2014 x 2015 - 2016 ) : ( 2012 + 2013 x 2014 )

= ( 4058210 - 2016 ) : ( 2012 + 4054182 )

= 4056194 : 4056194

= 1

﴾ 2014 x 2015 ‐ 2016 ﴿ : ﴾ 2012 + 2013 x 2014 ﴿

= ﴾ 4058210 ‐ 2016 ﴿ : ﴾ 2012 + 4054182 ﴿

= 4056194 : 4056194

= 1

 ( 2014 x 2015 - 2016 ) : (2012 + 2013 x 2014 )

= ( 2014 x ( 2013 + 2 ) - 2016 ) : ( 2012 + 2013 x 2014 )

= ( 2014 x 2013 + 2014 x 2 - 2016 ) : ( 2012 + 2013 x 2014 )

= ( 2014 x 2 - 2016 ) : 2012

=  ( 4028 - 2016 ) : 2012 

=      2012       : 2012

= 1 

Bài làm:

\(x=\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}\)

\(x=\frac{2012.2014.2015+2013.2013.2015+2014.2013.2014}{2013.2014.2015}\)

\(x=\frac{8165118520+8165120535+8165122548}{8169176730}\)

\(x=\frac{24495361603}{8169176730}\)

Học tốt!

>: đúng vậy ... mỗi cách đấy ! , nhưng @Đăng ... chép sai đề kìa 

\(x=\frac{2012}{2013}+\frac{2013}{2014}+\frac{2015}{2016}\)

\(=\frac{2012.2014.2016}{2013.2014.2016}+\frac{2013.2012.2016}{2014.2013.2016}+\frac{2015.2013.2014}{2016.2014.2013}\)

\(=\frac{2012.2014.2016+2013.2012.2016+2015.2013.2014}{2013.2014.2016}\)

\(=\frac{8169170688+8165114496+8169176790}{8173290912}\)

Để thế này cx đc >: chả ảnh hưởng j cả, mà sợ đáp án sai vì số dài ... xem lại hộ nhé ! 

\(\dfrac{x-1}{2012}+\dfrac{x-2}{2013}+\dfrac{x-3}{2014}=\dfrac{x-4}{2015}+\dfrac{x-5}{2016}+\dfrac{x-6}{2017}\)

\(\Leftrightarrow\left(\dfrac{x-1}{2012}+1\right)+\left(\dfrac{x-2}{2013}+1\right)+\left(\dfrac{x-3}{2014}+1\right)=\left(\dfrac{x-4}{2015}+1\right)+\left(\dfrac{x-5}{2016}+1\right)+\left(\dfrac{x-6}{2017}+1\right)\)

\(\Leftrightarrow\dfrac{x+2011}{2012}+\dfrac{x+2011}{2013}+\dfrac{x+2011}{2014}-\dfrac{x+2011}{2015}-\dfrac{x+2011}{2016}-\dfrac{x+2011}{2017}=0\)

\(\Leftrightarrow\left(x+2011\right)\left(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2015}-\dfrac{1}{2016}-\dfrac{1}{2017}\right)=0\)

\(\Leftrightarrow x=-2011\)( do \(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2015}-\dfrac{1}{2016}-\dfrac{1}{2017}\ne0\))

Ta có : \(\frac{x+5}{2012}+\frac{x+4}{2013}+\frac{x+3}{2014}=\frac{x+2}{2015}+\frac{x+1}{2016}+\frac{x}{2017}\)

\(\Rightarrow\frac{x+5}{2012}+1+\frac{x+4}{2013}+1+\frac{x+3}{2014}=\frac{x+2}{2015}+1+\frac{x+1}{2016}+1+\frac{x}{2017}+1\)

\(\Leftrightarrow\frac{x+2017}{2012}+\frac{x+2017}{2013}+\frac{x+2017}{2014}=\frac{x+2017}{2015}+\frac{x+2017}{2016}+\frac{x+2017}{2017}\)

\(\Leftrightarrow\frac{x+2017}{2012}+\frac{x+2017}{2013}+\frac{x+2017}{2014}-\frac{x+2017}{2015}-\frac{x+2017}{2016}-\frac{x+2017}{2017}=0\)

\(\Leftrightarrow\left(x+2017\right)\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)
\(\text{Mà }\)\(\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)\ne0\)

\(\text{Nên : }\) x + 2017 = 0 

=> x = -2017