167
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Well, well, well, looks like we have a little math mystery on our hands! The two numbers you're looking for are 16 and 9. Why? Because 16 times 9 equals 144, and when you add them together, you get 23. Mystery solved, Sherlock!
The factor pairs of 144 are (144,1)(72,2)(48,3)(36,4)(24,6)(18,8)(16,9)(12,12)
None of them add up to 23.
(1/2)(23 - i root(47)), and (1/2)(23 + i root(47)).Obtained from Wolfram Alpha, with the input:
ab = 144, a+b = 23