Ta có :
\(\frac{x-1}{27}+\frac{x-2}{26}+\frac{x-3}{25}+\frac{x-4}{24}=4\)
\(\Leftrightarrow\)\(\left(\frac{x-1}{27}-1\right)+\left(\frac{x-2}{26}-1\right)+\left(\frac{x-3}{25}-1\right)+\left(\frac{x-4}{24}-1\right)=4-4\) ( trừ 2 vế cho 4 )
\(\Leftrightarrow\)\(\frac{x-28}{27}+\frac{x-28}{26}+\frac{x-28}{25}+\frac{x-28}{24}=0\)
\(\Leftrightarrow\)\(\left(x-28\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}\right)=0\)
Vì \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}\ne0\)
Nên \(x-28=0\)
\(\Rightarrow\)\(x=28\)
Vậy \(x=28\)
Chúc bạn học tốt ~
\(x-\frac{1}{27}+x-\frac{2}{26}+x-\frac{3}{25}+x-\frac{4}{24}=4\)
\(\left(x+x+x+x\right)-\left(\frac{1}{27}+\frac{2}{26}+\frac{3}{25}+\frac{4}{24}\right)=4\)
\(4x-\frac{7031}{17550}=4\)
\(4x=4+\frac{7031}{17550}\)
\(x=\frac{4+\frac{7031}{17550}}{4}=1+\frac{\frac{7031}{17550}}{4}\)
\(x=1+\frac{7031}{70200}\)
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