Best Answer

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

Simplify

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

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

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80

One and seven.

The number .5 means half. So, if you take half of something, that is less than the entire thing, right? And half of half is a quarter. Multiplication only makes numbers larger when you multiply numbers that are greater than one. If you multiply by one the number doesn't change. If you multiply by less than one, you make the number smaller.

negative 3 and positive 4

A=x^2+10x+24 you need two numbers that will multiply to 24 and add to 10 (x+4) (x+6) 4 and 6 add up to 10 and multiply to equal 24 A = n^2+n-2 you need two numbers that will add up to one and multiply to -2 (n+2)(n-1) 2 and -1 add up to 1 and multiply to equal -2

Related questions

12

80

One and seven.

There are infinitely many pairs of numbers that will add to 105.8 and infinitely many pairs of numbers that will multiply to 105.8 but there are no pair that will add AND multiply. I do not think there are larger sets, but I could be wrong. One example of a triplet adding and multiplying to the same number is 1, 2 and 3. They add to 6 and multiply to 6.

The number .5 means half. So, if you take half of something, that is less than the entire thing, right? And half of half is a quarter. Multiplication only makes numbers larger when you multiply numbers that are greater than one. If you multiply by one the number doesn't change. If you multiply by less than one, you make the number smaller.

41

-9 and 10

-13

Yes, but you need two positive numbers less than one. 0.5 * 0.5 = 0.25 for instance. (half of a half is a quarter)

negative 3 and positive 4

-3.1 and 4.6

Multiply all the numbers together and then add 1.