two numbers; added make 10 multiplied make 20?

[nix-j-c]

i posted this in scince because it envolves maths but i was advised to repost this here!

a couple of years ago i'm sure that i worked out two numbers that when added make 10 and when multiplied make 20.

but i remember that it took me ages to do so does anyone know what these two numbers are?

i'm asking because someone brought it up again and i couldn't remember the answer and now its really annoying.

i've tried googling it but i can't find it. its possible that i never did work it out but i'm sure i at least came close. so if it is impossible what is the closest you can get? i'm trying not to be lazy, i just thought that someone might know the answer without having to work it out again.

[mohill]

The numbers are (5 + sq root of 5) and (5 - sq root of 5).
ie 5 + 2.236 and 5 - 2.236
ie 7.236 and 2.764
The working involves solving a quadratic equation.
If you want the working let me know and I'll set it out'
Cheers

[factor-fiction]

Yes, I agree with mohill. You need to use the quadratic formula:

x=
-b�√(b�-4ac)
2a

Let the two numbers be represented by x and y
So xy=20 and x+y=10 (i.e. y= 10-x)

Combining the two:
x(10-x)=20
10x-x� -20=0
x�-10x +20 =0
x=[10 �√ (100-80)]/2
= 5�√5

[nix-j-c]

the first time i did it we hadn't learnt that formulae but i learnt it recently but never thought to use it for this.

thanks.