Does a wife become divorced by uttering the words once and by writing them three times, and what is the ruling on taking her back?

Your first divorce (talaq) of your wife is valid. As for the three divorces (talaqat) you wrote, there is a detailed explanation: If your intention was to repeat the divorce to affirm the first one with the subsequent two, then it is considered one divorce added to your first one. However, if your intention was to initiate an independent divorce, then the majority of scholars, including the four Imams, consider them three divorces, by which your wife becomes irrevocably divorced from you. You must refer to the Sharia courts in your country to ascertain the true situation.