What numbers add to one and multiply to one half?

Updated: 11/1/2022
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11y ago

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Let x = 1st number and y = 2nd number

x + y = 1 (they add to 1)

xy = 1/2 ( multiply to one half)

rearrange top equation to y = (1 - x) and substitute this into the 2nd

x(1-x) = 1/2 I don't like to work with fractions so multiply by 2 and use the distributive property

2x - 2x2 = 1 rearrange into standard form for a quadratic

2x2 - 2x + 1 = 0

This will not factor using integers. Use the quadratic formula to solve it.

x = (2 + (sq root)(4 - 8))/4 and x = (2 - (sq root)(4 - 8))/4

x = (2 + (sq root)(-4))/4 and x = (2 - (sq root)(-4))/4


x = (1 + i)/2 and x = (1 - i)/2

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Q: What numbers add to one and multiply to one half?
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