'Access denied for user 'root'@'localhost' (using password: NO)'

[root@red-1 mysql]# /etc/init.d/mysqld stop
Stopping mysqld:                                           [  OK  ]
[root@red-1 mysql]# mysqld_safe --skip-grant-tables &
[1] 22881
[root@red-1 mysql]# 130327 12:33:15 mysqld_safe Logging to '/var/log/mysqld.log'.
130327 12:33:15 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql

[root@red-1 mysql]# mysql -u root
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.1.61 Source distribution

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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> use mysql;
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> update user set password=PASSWORD('1234') where User='root';
Query OK, 3 rows affected (0.00 sec)
Rows matched: 3  Changed: 3  Warnings: 0

mysql> flush privileges;
Query OK, 0 rows affected (0.00 sec)

mysql> quit
Bye