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a )
\(\Rightarrow\frac{x-100}{24}-1+\frac{x-98}{26}-1+\frac{x-96}{26}-1=0\)
\(\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)
\(\left(x-124\right)\left(\frac{1}{26}+\frac{1}{24}+\frac{1}{28}\right)=0\)
\(\Rightarrow x-124=0\Rightarrow x=124\)
ta co (x-2163)(1/2011+1/28+1/124)=0
vi 1/2011+1/28+1/124khac0
x-2163=0
x=2163
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
Ta có:\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)
\(\Rightarrow\)\(\frac{91x-100.91}{91.24}+\frac{84x-84.98}{26.84}+\frac{78x-96.78}{78.28}\)
=\(\frac{91x-9100+84x-8232+78x-7488}{2184}\)
=\(\frac{91x+84x+78x-9100-8232-7488}{2184}\)
=\(\frac{x\left(91+84+78\right)-\left(9100+8232+7488\right)}{2184}\)
=\(\frac{x253-24820}{2184}=3\)
\(\Rightarrow\)x253- 24820 =6552
\(\Rightarrow\)x253= 31372
\(\Rightarrow\)x = 124
\(\frac{x-100}{24}+\frac{x-98}{+26}+\frac{x-96}{28}=3\)
\(=\frac{\left(x-100\right)}{24}+\frac{\left(x-98\right)}{26}+\frac{\left(x-96\right)}{28}-1=0\)
\(\Leftrightarrow\frac{\left(x-100\right)}{24-1}+\frac{\left(x-98\right)}{26-1}+\frac{\left(x-96\right)}{28-1}=0\)
\(\Leftrightarrow\left(x-124\right)\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)=0\)
Vì: \(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\ne0\)
\(\Rightarrow x-124=0\)
\(\Rightarrow x=124-0\)
\(\Rightarrow x=124\)