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15 and -3

Q: What 2 numbers multiplied together equal negative 45 but added together equal 12?

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-8 and 7

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24

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x=-11 y=1 or x=1 y=-11

No two numbers exist.for the two numbers to be added to be negative and multiplied to be positive, both numbers must be negative, and the highest possible multiplication for two numbers added to -12 would be (-6 and -6) but multiplied, yields 36. So, no such numbers would exist.