Failure to resign also could create the perception for the rank and file that such behavior is acceptable.
At FBI headquarters, spokesman Paul Bresson declined to comment on the information that the affair had been discovered in the course of an investigation by the bureau.
Holly Petraeus is known for her work helping military families. She joined the new Consumer Financial Protection Bureau to set up an office dedicated to helping service members with financial issues.
Though Obama made no direct mention of Petraeus' reason for resigning, he offered his thoughts and prayers to the general and his wife, saying that Holly Petraeus had "done so much to help military families through her own work. I wish them the very best at this difficult time."
Petraeus, who became CIA director in September 2011, was known as a shrewd thinker and hard-charging competitor. His management style was recently lauded in a Newsweek article by Broadwell.
The article listed Petraeus' "rules for living." No. 5 was: "We all make mistakes. The key is to recognize them, to learn from them, and to take off the rear view mirrors — drive on and avoid making them again."
In the preface to her book, Broadwell said she first met Petraeus in the spring of 2006. She was a graduate student at the Kennedy School of Government at Harvard, and he was visiting the university to discuss his experiences in Iraq and a new counterinsurgency manual he was working on.
She had graduated from West Point with academic, fitness, and leadership honors, according to a biography posted on her publisher's website that lists authors available for speaking engagements.
The biography said she had "lived, worked, or traveled in more than 60 countries during more than 15 years of military service and work in geopolitical analysis and counterterrorism and counterinsurgency operations." It said she had spent time with the U.S. intelligence community, U.S. Special Operations Command and FBI Joint Terrorism Task Forces.
Harvard invited some students to meet with Petraeus, and Broadwell was among them because of her military background, which she wrote included being recalled to active duty three times to work on counterterrorism issues after the Sept. 11 attacks.
"I had since joined the Army Reserve and begun graduate studies with the intent of returning either to active duty or to the policy world," she wrote in the preface. She introduced herself and described her research interests. He gave her his card and offered to connect her with others working on the same issues.
"I later discovered that he was famous for this type of mentoring and networking, especially with aspiring soldier-scholars. He immediately responded to the email, inviting me to bounce ideas off him. I took full advantage of his open-door policy to seek insight and share perspectives," Broadwell wrote.
In 2008, she wrote, she was pursuing a Ph.D. in public policy and embarking on a case study of Petraeus' leadership. At one point, she said, he invited her for a run along the Potomac River with his team while he was in Washington.
"I'd earned varsity letters in cross-country and indoor and outdoor track and finished at the top of my class for athletics at West Point; I wanted to see if he could keep stride during an interview. Instead it became a test for me." He eventually increased the pace "until the talk turned to heavy breathing and we reached a 6-minute-per-mile pace. It was a signature Petraeus move. I think I passed the test, but I didn't bother to transcribe the interview."
After Obama put Petraeus in charge in Afghanistan in 2010, Broadwell decided to expand her research into an authorized biography.
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