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x + y = 3, y = -x + 3

xy = 152

x(-x + 3) = 152

-x2 + 3x = 152

x2 - 3x = -152 form the square

x2 - 3x + (3/2)2 = (3/2)2 - 152

(x - 3/2)2 = 9/4 - 152

x - 3/2 = ±√[(9 - 152*4)/4]

x = 3/2 ± (√-599)/2

x = (3 ± i√599)/2

x = (3 + i√599)/2 or x = (3 - i√599)/2

y = 3 - x

y = 3 - (3 + i√599)/2

y = (6 - 3 - i√599)/2

y = (3 - i√599)/2 or y = (3 + i√599)/2

Check:

[(3 + i√599)/2][(3 - i√599)/2] = [32 - (i√599)2]/4 = (9 - 599i2)/4 =( 9 + 599)/4 = 608/4 = 152

(3 + i√599)/2 + (3 - i√599)/2 = (3 + i√599 + 3 - i√599)/2 = 6/2 = 3

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Q: What two numbers multiplied equal 152 with a sum of 3?
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