MySQL root密码重置报错

[root@mysql var]# mysqladmin -u root password '123456'

mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user 'root'@'localhost' (using password: NO)'

[root@mysql var]# /etc/init.d/mysqld stop

Shutting down MySQL.... SUCCESS!

[root@mysql var]# mysqld_safe --skip-grant-tables &
/opt/mysql/product/5.5.25a/bin/mysqld_safe --skip-grant-tables &

[1] 10912

[root@mysql var]# /usr/bin/mysql -uroot -p 
【注释，在下面的要求你输入密码的时候，你不用管，直接回车键一敲就过去了】

Enter password:
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 48
Server version: 5.1.41-log Source distribution
 
Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
  
mysql> use mysql;
Database changed

mysql> update user set password=password("guxxxxxahyVh") where user='root' and host='localhost';

Query OK, 1 row affected (0.00 sec)
Rows matched: 1  Changed: 1  Warnings: 0
 
mysql> flush privileges;
Query OK, 0 rows affected (0.00 sec)
 
mysql> quit
Bye

[root@mysql var]# service mysqld restart

[root@app60 mysqld]#  /usr/bin/mysql -uroot -p

Enter password:
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111)
[root@app60 mysqld]#

[root@app60 mysqld]#  /usr/bin/mysql -uroot -p --socket=/opt/mysqldata/mysql.sock

Enter password:
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 6
Server version: 5.1.69 Source distribution

[root@app60 mysqld]# vi /etc/init.d/mysqld
.....
get_mysql_option mysqld datadir "/var/lib/mysql"
datadir="$result"
get_mysql_option mysqld socket "$datadir/mysql.sock"
socketfile="$result"
get_mysql_option mysqld_safe log-error "/var/log/mysqld.log"
errlogfile="$result"
get_mysql_option mysqld_safe pid-file "/opt/mysqldata/mysqld.pid"    # '/var/run/mysqld/mysqld.pid' 原始值,这里修改成别的路径/opt/mysqldata/mysqld.pid
mypidfile="$result"
.....