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Q: What two numbers add up to 23 and multiply to 50?

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83

23

-397

There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.

There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)

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