\(\frac{x-28-124}{2011}\)\(+\frac{x-124-2011}{28}\)\(+\frac{x-2011-28}{124}\)\(=3\)
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ta co (x-2163)(1/2011+1/28+1/124)=0
vi 1/2011+1/28+1/124khac0
x-2163=0
x=2163
\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
<=> \(\left(\frac{x-152}{2011}-1\right)+\left(\frac{x-2135}{28}-1\right)+\left(\frac{x-2039}{124}-1\right)=0\)
<=> \(\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)
<=> \(\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)
<=> \(x-2163=0\)(vì \(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\ne0\)
<=> \(x=2163\)
\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
<=> \(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}-3=0\)
<=> \(\left(\frac{x-28-124}{2011}-1\right)+\left(\frac{x-124-2011}{28}-1\right)+\left(\frac{x-2011-28}{124}-1\right)=0\)
<=> \(\frac{x-28-124-2011}{2011}+\frac{x-124-2011-28}{28}+\frac{x-2011-28-124}{124}=0\)
<=> \(\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)
<=> \(\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)
Vì \(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\ne0\)
=> \(x-2163=0\)
=> \(x=2163\)
a )
\(\Rightarrow\frac{x-100}{24}-1+\frac{x-98}{26}-1+\frac{x-96}{26}-1=0\)
\(\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)
\(\left(x-124\right)\left(\frac{1}{26}+\frac{1}{24}+\frac{1}{28}\right)=0\)
\(\Rightarrow x-124=0\Rightarrow x=124\)
b) (4x -1)2 = (1-4x)4 (1)
Vì (1 - 4x) = (4x - 1)
\(\Rightarrow\)(1 - 4x)4 = [ -( 4x -1)4 ]
Vì (1-4x)4 = ( 4x - 1)4
Do đó (1) có dạng :
(4x - 1)2 = (4x - 1)2
Đặt 4x - 1 = x, ta có :
x2 = x4
x2 ( 1 - x2 ) = 0
\(\Rightarrow\)\(\orbr{\begin{cases}x=0\\x^2=\orbr{\begin{cases}1^2\\\left(-1\right)^2\end{cases}}\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=\orbr{\begin{cases}x=1\\x=-1\end{cases}}\end{cases}}\)
Thay x = 4x -1 = 0
x = \(\frac{1}{4}\)
- x = 1 \(\Leftrightarrow\) 4x - 1 = 1
x = \(\frac{1}{2}\)
- x = -1 \(\Leftrightarrow\) 4x -1 = -1
x = 0
Vậy x = \(\frac{1}{2}\) hoặc x = 0