mk giải cho mà saI CÓ đc tiền k

\(\frac{\left(2007-x\right)^2+\left(2007-x\right)\left(x-2008\right)+\left(x-2008\right)^2}{\left(2007-x\right)^2-\left(2007-x\right)\left(x-2008\right)+\left(x-2008\right)^2}=\frac{19}{49}\)

điểu kiện xác định x khác 2007 and x khác 2008

Đặt a=x-2008 ( a khác 0 ,) ta có hệ thức

\(\frac{\left(a+1\right)^2-\left(a+1\right)a+a^2}{\left(a+1\right)^2+\left(a+1\right)a+a^2}=\frac{19}{49}\)

=>\(\frac{a^2+a+1}{3a^2+3a+1}=\frac{19}{49}\)

=>\(49a^2+49a+49=57a^2+57a+19\)

=>\(8a^2+8a-30=0\)

=>\(\left(2a-1\right)^2-4^2=0=>\left(2a-3\right)\left(2a+5\right)=0\)

=>\(\orbr{\begin{cases}a=\frac{3}{2}\\a=-\frac{5}{2}\end{cases}}\)(Thỏa mãn điều kiện)

Tự thay a xong suy ra x nhá 

Mệt lắm r

bài khó thế 

\(???\)\(\frac{19}{29}ak\)

ko sao , bạn cx nhân chéo lên tương tự như cách làm của mình xong => ra a mà làm nha . Hihi ..^^

đầu bài có sai k ạ???

de bai hinh nhu khong sai ban a

Theo to:

A>B

\(A=\frac{2006+2007}{2006.2007}=\frac{2006}{2006.2007}+\frac{2007}{2006.2007}=\frac{1}{2007}+\frac{1}{2006}\)

\(B=\frac{2007+2008}{2007.2008}=\frac{2007}{2007.2008}+\frac{2008}{2007.2008}=\frac{1}{2008}+\frac{1}{2007}\)

Vì \(\frac{1}{2007}+\frac{1}{2006}>\frac{1}{2008}+\frac{1}{2007}\)

=> \(A>B\)

Ta có : \(\frac{x+2011}{1}+\frac{x+2008}{2}+\frac{x+2007}{3}+\frac{x+2011}{5}=-15\)

\(\Rightarrow\left(\frac{x+2011}{1}+5\right)+\left(\frac{x+2008}{2}+4\right)+\left(\frac{x+2007}{3}+3\right)+\left(\frac{x+2008}{4}+2\right)+\left(\frac{x+2011}{5}+1\right)\)

\(=0\)

=> \(\frac{x+2016}{1}+\frac{x+2016}{2}+\frac{x+2016}{3}+\frac{x+2016}{4}+\frac{x+2016}{5}=0\)

=> \(\left(x+2016\right)\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)=0\)

Vì \(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\ne0\)

=> x + 2016 = 0

=> x = -2016

Vậy x = -2016

x+(x+2008)1/2+(x+2007)1/3+(x+2008)1/4+(x+2011)1/5=-15-2011=-2026

<=> x+x/2+1004+x/3+669+x/4+502+x/5+2011/5=-2026

<=>x+x/2+x/3+x/4+x/5+2011/5=-2026-1004-669-502=-4201

<=>x(1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5))=-4201-(2011)/(5)=-23016/5

<=>x=-23016/5:(1+1/2+1/3+1/4+1/5)=-2016

           Bài làm :

Ta có :

 \(\frac{x+2011}{1}+\frac{x+2008}{2}+\frac{x+2007}{3}+\frac{x+2011}{5}=-15\)

\(\Rightarrow\left(\frac{x+2011}{1}+5\right)+\left(\frac{x+2008}{2}+4\right)+\left(\frac{x+2007}{3}+3\right)+\left(\frac{x+2008}{4}+2\right)+\left(\frac{x+2011}{5}+1\right)\)

\(=0\)

 \(\Leftrightarrow\frac{x+2016}{1}+\frac{x+2016}{2}+\frac{x+2016}{3}+\frac{x+2016}{4}+\frac{x+2016}{5}=0\)

 \(\Leftrightarrow\left(x+2016\right)\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)=0\)

 \(\text{Vì : }1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}>0\)

\(\Rightarrow x+2016=0\)

\(\Leftrightarrow x=-2016\)

Vậy x=-2016