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Let the middle one be n, then:

(n - 2)(n + 2) = 3n + 6

→ n² - 4 = 3n + 6

→ n² - 3n - 10 = 0

→ (n + 2)(n - 5) = 0

→ n = -2 or 5

-2 can be discounted as n is odd

→ n = 5

→ largest of the three odd numbers is 5 + 2 = 7.

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