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ALEX’S BIG A-POLOGY

The reconciliation between A-Rod and Yankee brass began last week with two simple words: I’m sorry.

With his public image taking a hit, a humbled Alex Rodri guez flew to Tampa without his agent to meet Hank and Hal Steinbrenner.

“There were mistakes made by his agent [Scott Boras],” Hank Steinbrenner told The Post yesterday. “[Rodriguez] very strongly apologized.”

The mea culpa was what the Steinbrenners needed to hear before hashing out a soon-to-be-inked 10-year contract with the slugger valued at a record $300 million.

“I needed to be convinced that he really wanted to be a Yankee, and he really does,” Hank Steinbrenner said. “He wanted me to know that.”

A-Rod‘s penance to the Pinstripes capped three weeks of a messy breakup with the team, which saw the third baseman heed the advice of his combative agent and opt out of the last three years of his contract.

“This year was a magical season,” Rodriguez told MLB.com. “The way things went, we came up a little short at the end. But other than that, I’m happy with the way the year went. My wife and I finally feel like we’re New Yorkers.”

The Yankees had offered the slugger five-year extension for $140 million.

“We reached out to him, and then he didn’t call us back,” Steinbrenner said. “Scott did mess things up.”

Boras announced that A-Rod was opting for free agency during the late innings of the final game of the World Series. The frosty relations between the Yankees and A-Rod‘s camp didn’t start to thaw until days later, when the slugger asked billionaire buddy Warren Buffett how he could ingratiate himself with the Steinbrenners.

The financial whiz and avid baseball fan told A-Rod to approach the clan without Boras, The Wall Street Journal reported on its Web site yesterday.

Rodriguez then contacted the Yankees through friend John Mallory, a Goldman Sachs executive who handles a Steinbrenner account.

Mallory passed the word on to Goldman partner Gerry Cardinale, head of media and telecommunications investments, who told Yankee President Randy Levine that Rodriguez was filled with remorse, according to the Journal.

“I don’t know why. Maybe he was shy about calling back,” Steinbrenner told The Post, when asked why Rodriguez did not approach the team directly.

Rodriguez is close to finalizing a 10-year deal worth $275 million and is negotiating a possible revenue-sharing deal that could push the contract beyond $300 million.

brad.hamilton@nypost.com