Place artichokes, potatoes, and carrot in a large bowl, and toss gently to combine. Lightly spoon flour into a dry measuring cup; level with a knife. Add flour, salt, and pepper to artichoke mixture; toss gently to combine. Add egg and egg white; stir just until combined.
Heat half of oil in a large nonstick skillet over medium-high heat. Spoon about 1/4 cup artichoke mixture for each of 9 latkes into pan. Cook 3 minutes on each side or until browned. Remove from pan. Repeat procedure with remaining oil and artichoke mixture. Serve with sour cream.