a) Ta có: \(\left(4x-1\right)^2=\left(1-4x\right)^2\)

\(\Leftrightarrow\left(4x-1\right)^2-\left(1-4x\right)^2=0\)

\(\Leftrightarrow\left(4x-1-1+4x\right)\left(4x-1+1-4x\right)=0\)

\(\Leftrightarrow0\cdot x=0\)(luôn đúng)

Vậy: \(x\in R\)

b) Ta có: \(\dfrac{x-100}{24}+\dfrac{x-98}{26}+\dfrac{x-96}{28}=3\)

\(\Leftrightarrow\dfrac{x-100}{24}-1+\dfrac{x-98}{26}-1+\dfrac{x-96}{28}-1=0\)

\(\Leftrightarrow\dfrac{x-124}{24}+\dfrac{x-124}{26}+\dfrac{x-124}{28}=0\)

\(\Leftrightarrow\left(x-124\right)\cdot\left(\dfrac{1}{24}+\dfrac{1}{26}+\dfrac{1}{28}\right)=0\)

mà \(\dfrac{1}{24}+\dfrac{1}{16}+\dfrac{1}{28}>0\)

nên x-124=0

hay x=124

Vậy: x=124

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: \(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\ne0\)

\(\Rightarrow x-124=0\)

\(\Rightarrow x=124-0\)

\(\Rightarrow x=124\)

Ta có :\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)

           \(\Rightarrow\frac{91x-100.91}{91.24}+\frac{84x-84.98}{26.84}+\frac{78x-96.78}{78.28}\)

           \(=\frac{91x-100.91+84x-8232+78x-7488}{2184}\)

            \(=\frac{91x+84x+78x-9100-8232-7488}{2184}\)

             \(=\frac{x\left(91+84+78\right)-\left(9100+8232+7488\right)}{2184}\)

               \(=\frac{x253-24820}{2184}=3\)

                 \(\Rightarrow x253-24820=6552\)

                 \(\Rightarrow x253=31372\)

                  \(\Rightarrow x=124\)

\(\Rightarrow\frac{x-100}{24}-1+\frac{x-98}{26}-1+\frac{x-96}{28}-1=3-1-1-1=0\)

\(\Rightarrow\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)

\(\Rightarrow\left(x-124\right)\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)=0\)

\(\Rightarrow x-124=0\) ( vì 1/24 + 1/26 + 1/28 khác 0)

=> x = 124 

(x-100)/24 + (x-98)/26 + (x-96)/28 = 3 
<=> (x - 100)/24 -1 + (x-98)/26-1 (x-96)/28 -1 = 0 
<=>(x-124)/24 + (x-124)/26 + (x - 124)/28 =0 
<=>(x - 124) (1/24+1/26+1/28) = 0 
vì 1/24+1/26+1/28 khác 0 
=> x - 124 = 0 
=> x = 124 
2) (x-1)/65 + (x-3)/63 = (x-5)/61 + (x-7)/59 
tương tự: 
(x-1)/65 -1 +(x -3)/63 -1 = (x-5)/61-1 + (x-7)/59 -1 
rút gọn được: 
(x - 66).(1/65 + 1/63) = (x -66).(1/61 + 1/59) 
(x - 66).(1/65 + 1/63 - 1/61 -1/59) = 0 
=> x = 66 (lý luận tương tự câu trên) 

a . x= 124

b.x=66

\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)

\(\Leftrightarrow\frac{x-100}{24}-1+\frac{x-98}{26}-1+\frac{x-96}{28}-1=0\)

\(\Leftrightarrow\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)

\(\Leftrightarrow\left(x-124\right)\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)=0\)

Mà 1/24+1/26+1/28 khác 0

\(\Leftrightarrow x-124=0\Leftrightarrow x=124\)

\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)

\(\Leftrightarrow\frac{x-100}{24}-1+\frac{x-98}{26}-1+\frac{x-96}{28}-1=0\)

\(\Leftrightarrow\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)

\(\Leftrightarrow\left(x-124\right)\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)=0\)

Mà \(\frac{1}{24};\frac{1}{26};\frac{1}{28}\)khác \(0\)

\(\Leftrightarrow x-124=0\Leftrightarrow x=124\)

\(\frac{x}{24}-\frac{25}{6}+\frac{x}{26}-\frac{49}{13}+\frac{x}{28}-\frac{24}{7}=3\)

\(x\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)-\left(\frac{25}{6}+\frac{49}{13}+\frac{24}{7}\right)=3\)

\(x\cdot\frac{253}{2184}=\frac{7843}{546}\)

\(x=124\)

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) 

\(\frac{x-28-124}{2011}-1+\frac{x-124-2011}{28}-1+\frac{x-2011-28}{124}-1=0\)

\(\Rightarrow\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)

\(\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)

=) x - 2163 =0

x= 2163