Ta có :
| x - 1 | \(\ge\)0 ; | x - 2 | \(\ge\)0 ; | x - 3 | \(\ge\)0 ; ... ; | x - 100 | \(\ge\)0
\(\Rightarrow\)| x - 1 | + | x - 2 | + ... + | x - 100 | \(\ge\)0
\(\Leftrightarrow\)| x - 1 | = x - 1 ; | x - 2 | = x - 2 ; ... ; | x - 100 | = x - 100
\(\Leftrightarrow\)( x - 1 ) + ( x - 2 ) + ... + ( x - 100 ) = 2500
( x + x + ... + x ) - ( 1 + 2 + ... + 100 ) = 2500
100x - 5050 = 2500
100x = 7550
\(\Rightarrow\)x = 75,5