(x-101)/86 - 1+ (x-103)/84 - 1 + (x-105)/82 - 1 = 0
<=>(x-187)/86+ (x-187)/84 + (x-187)/82 = 0
<=> (x-187)(1/86+1/84+1/82)=0
mà 1/86+1/84+1/82 khác 0 suy ra x-187=0
x=187
\(\frac{x-101}{86}+\frac{x-103}{84}+\frac{x-105}{82}=3\)
\(\Leftrightarrow\) \(\frac{x-101}{86}+\frac{x-103}{84}+\frac{x-105}{82}-3=0\)
\(\Leftrightarrow\) \(\left(\frac{x-101}{86}-1\right)+\left(\frac{x-103}{84}-1\right)+\left(\frac{x-105}{82}-1\right)=0\)
\(\Leftrightarrow\) \(\frac{x-187}{86}+\frac{x-187}{84}+\frac{x-187}{82}=0\)
\(\Leftrightarrow\) \(\left(x-187\right)\left(\frac{1}{86}+\frac{1}{84}+\frac{1}{82}\right)=0\) \(\left(\text{*}\right)\)
Vì \(\frac{1}{86}+\frac{1}{84}+\frac{1}{82}\ne0\) nên từ \(\left(\text{*}\right)\) suy ra \(x-187=0\) \(\Leftrightarrow\) \(x=187\)
Vậy, tập nghiệm của pt trên là \(S=\left\{187\right\}\)
