Hỏi đáp bài tập

Hãy tham gia nhóm Học sinh Hoc24OLM

CTV

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

Đọc tiếp...

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

Đọc tiếp...

           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

Đọc tiếp...