What are two numbers that equal 12 when multiplied together but equal 15 when added together?

Answer 1

This is not possible. I know that this isn't possible since the only two pairs of numbers that can be multiplied together to equal 12 are:

6x2=12, 6+2=8

4x3=12, 4+3=7

12x1=12, 12+1=13

None of these equal 12 as shown above.

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0.848 and 14.152 (to 3 decimal places only)

This is perfectly possible. The question did not specify that the numbers had to be integers (as inferred from the above answer). We solve this using algebra (and not by writing down all possible combinations of numbers).

We can write two equations from the given information:

1. x * y = 12

2. x + y = 15

We can now rewrite 2. as:

3. x = -y + 15

We can now substitute this value for x back into 1. to give:

4. (-y + 15) * y = 12

We now multiply out the bracket:

-y2 + 15y = 12

We now subtract 12 from both sides of the equation so that we have an equation that equals 0:

-y2 + 15y - 12 = 0

Now that we have written the equation in the form of a quadratic equation we can use the below quadratic formula to solve for the roots of y.

For an equation in the form of ay2 + by + c= 0 then:

y = (-b + OR - (b2 - (4ac))1/2) / 2a

y = (-15 + or - ((152 - (4 * -1 * -12))1/2) / 2 * -1

y = (-15 + or - (225 - 48)1/2) / -2

y = (-15 + or - 1771/2) / -2

You can now calculate this to the required level of accuracy as desired.

I will write the answer accurate to 3 decimal places only:

y = 0.848 and 14.152

These numbers are the two roots of the equation and the answer to the question. They are only provided accurate to 3 decimal places however (for my own convenience) and so if you substitute them back into the original equations they will not multiply to give exactly 12. This is due only to the level of accuracy provided in this answer and not due to any error in the maths.

(Note: x1/2 is an alternate way of writing "the square root of x". I have done this because I do not know how to write a square root symbol on this website.)