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\(\frac{x-2016}{100}+\frac{x-2014}{102}+\frac{x-2016}{104}+...+\frac{x-2}{2114}=1008\)
\(\Rightarrow\frac{x-2016}{100}-1+\frac{x-2014}{102}-1+...+\frac{x-2}{2114}-1=0\)
\(\Rightarrow\frac{x-2116}{100}+\frac{x-2116}{102}+...+\frac{x-2116}{2114}=0\)
\(\Rightarrow\left(x-2116\right)\left(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\right)=0\)
mà \(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\ne0\)
\(\Rightarrow x-2116=0\)
\(\Rightarrow x=2116\)
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 \(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\ne0\)
\(=>x-2116=0\)
\(=>x=2116\)
\(\frac{x+2}{327}+\frac{x+3}{326}+....+\frac{x+349}{5}=\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+329}{5}+4=\left(\frac{x+2}{327}+1\right)+\left(\frac{x+3}{326}+1\right)+\left(\frac{x+4}{325}+1\right)+\left(\frac{x+5}{324}+1\right)+\frac{x+329}{5}=\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=\left(x+329\right)\left(\frac{1}{327}+\frac{1}{326}+....+\frac{1}{324}+\frac{1}{5}\right)=0\Rightarrow x+329=0\Leftrightarrow x=-329\)
Bạn tham khảo tại đây nhé: Câu hỏi của trần như.
Chúc bạn học tốt!
\(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0.\)
\(1+\frac{x+2}{327}+1+\frac{x+3}{326}+1+\frac{x+4}{325}+1+\frac{x+5}{324}-4+\frac{x+349}{5}=0\)
\(\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=0\)
\(\left(x+329\right).\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)=0\)
\(\Rightarrow x+329=0\)
\(\Rightarrow x=-329\)
Study well
\(\Rightarrow\frac{x+2}{327}+1+\frac{x+3}{326}+1+\frac{x+4}{325}+1+\frac{x+5}{324}+1+\frac{x+349}{5}-4=0\)
\(\Rightarrow\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=0\)
\(\Rightarrow\left(x+329\right).\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)=0\)
Mà \(\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)\ne0\)
Nên \(x+329=0\Rightarrow x=-329\)
Vậy \(x=-329\)
Chúc bạn học tốt !!!
Ta có: \(\frac{xy}{x+y}=\frac{yz}{y+z}=\frac{zx}{z+x}\)\(\Rightarrow\frac{xyz}{z\left(x+y\right)}=\frac{xyz}{x\left(y+z\right)}=\frac{xyz}{y\left(z+x\right)}\)\(\Rightarrow z\left(x+y\right)=x\left(y+z\right)=y\left(z+x\right)\)\(\Rightarrow zx+zy=xy+xz=yz+xy\)
Ta có: zx + zy = xy + xz => zy = xy => z = x (1)
Ta có: x - z = x - x = 0
Từ \(\frac{x-2016}{100}\rightarrow\frac{x-2}{2114}\) có tất cả \(1008\) số.
Ta có: \(\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}=1008\)
\(\Leftrightarrow\frac{x-2016}{100}+\frac{x-2014}{102}+...+\frac{x-2}{2114}-1008=1008-1008\)
\(\Leftrightarrow\left(\frac{x-2016}{100}-1\right)+\left(\frac{x-2014}{102}-1\right)+...+\left(\frac{x-2}{2114}-1\right)=0\) (*)
\(\Leftrightarrow\frac{x-2116}{100}+\frac{x-2116}{102}+...+\frac{x-2116}{2114}=0\)
\(\Leftrightarrow\left(x-2116\right)\left(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\right)=0\)
Vì \(\frac{1}{100}+\frac{1}{102}+...+\frac{1}{2114}\ne0\)
Nên từ pt (*) \(\Leftrightarrow x-2116=0\Leftrightarrow x=2116\)
Vậy...
Pạn là Wjbu Zen chăng???