mysql Access denied for user ‘root’@’localhost’ (using passw_MySQL

[root@www ~]# mysql -u root -p
Enter password: 
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

[root@www ~]# service mysqld stop   #先关闭mysql服务
Stopping mysqld:                      [ OK ]
[root@www ~]# mysql
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)
[root@www ~]# mysql -u root -p      #关闭服务后又出现如下问题
Enter password: 
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)
[root@www ~]# mysql -u root mysql    #键入此命令进入mysql
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.1.73 Source distribution
Copyright (c) 2000, 2013, Oracle and/or its affiliates. All rights reserved.
Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.
Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
mysql> update user set password=password('123') where user='root' and host='localhost';  ---->修改root的密码
Query OK, 1 row affected (0.04 sec)
Rows matched: 1 Changed: 1 Warnings: 0
mysql> flush priviledge;
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'priviledge' at line 1
mysql> flush privileges;
Query OK, 0 rows affected (0.00 sec)
mysql> \q
Bye
[root@www ~]# mysql -u root -p           ------>重新进入
Enter password: 
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 2
Server version: 5.1.73 Source distribution
Copyright (c) 2000, 2013, Oracle and/or its affiliates. All rights reserved.
Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.
Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
mysql> \q
Bye