Question

[Minh Pool]

Mn oi, helppp meee!!! :"((

Find x such that:

 \(\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}=1008\)

*Tạm dịch*( À mà dịch mỗi dòng trên ak :))

Tìm x sao cho: 

\(\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}=1008\)

@ Mn nhớ ghi cách giải hoặc đáp án thui cũng đc nha!!! :>

< ~ ~ ~ Cảm Ơn mn Rất Nhìu Nhoaa!!! ~ ~ ~ >

~ Arigatou gozaimasu ~ :3

Answer 1

[Thu Huệ]

\(\frac{x-2016}{100}+\frac{x-2014}{102}+\frac{x-2016}{104}+...+\frac{x-2}{2114}=1008\)

\(\Rightarrow\frac{x-2016}{100}-1+\frac{x-2014}{102}-1+...+\frac{x-2}{2114}-1=0\)

\(\Rightarrow\frac{x-2116}{100}+\frac{x-2116}{102}+...+\frac{x-2116}{2114}=0\)

\(\Rightarrow\left(x-2116\right)\left(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\right)=0\)

mà \(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\ne0\)

\(\Rightarrow x-2116=0\)

\(\Rightarrow x=2116\)

Answer 2

[Napkin ( Fire Smoke Team )]

P/s màu mè ghê ha =))

\(\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}=1008\)

\(=>\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}-1008=0\)

\(=>\frac{x-2016}{100}-1+\frac{x-2014}{102}-1+...+\frac{x-2}{2114}-1=0\)

\(=>\frac{x-2116}{100}+\frac{x-2116}{102}+...+\frac{x-2116}{2114}=0\)

\(=>\left(x-2116\right).\left(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\right)=0\)

Do \(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\ne0\)

\(=>x-2116=0\)

\(=>x=2116\)