numbers added make 10, timesed make 20

[nix-j-c]

i know this is more of a maths question but there isn't a maths section and many science people are good at maths.

what two numbers when added make 10 but when timesed make 20? i learnt it a couple of years ago and i was asked it again and i couldn't rememebr it and its really anoying me now. i've tried googling it but i can't find anything.

[dzug]

I'd say it was a trick question rather than maths/science. Quizzes and puzzles might be better.

[nix-j-c]

no i'm sure i work it out a couple of years ago.
the two numbers had loads of decimal places and thats why i'm asking if anyone knows them rather than working it out myself.

[mohill]

check my solution in Q and P

[vascop]

The answer is 5+sqrt(5) and 5-sqrt(5).
sqrt(5) means the square root of 5.

[fo3nix]

This can easily be solved, like this:

The two numbers you want to find can be named a and b. So you have two equations:

a + b = 10
a * b = 20

You have two equations and two unknowns, so your problem is solvable.

Here's the answers:

a=5-Sqrt[5], b=5+Sqrt[5]

(a and b can of course be interchanged.)

[vascop]

fo3nx
To quote from your post
"You have two equations and two unknowns, so your problem is solvable. "

But then you didn't go on to show how to solve it!

If the original poster is interested in how to solve it then here goes:
if a + b =10 then a=10-b.
substitute in the second equation (a*b=20) for 'a' gives
(10-b)*b=20 or
10b-b^2=20
re-arranging gives:
b^2-10b+20=0
So this is a quadratic equation for b. Therefore
b=(10+/-sqrt(100-80))/2 (+/- means plus or minus)
so b=(10+/-sqrt(20))/2
b=5+/-sqrt(5) since sqrt(20)=sqrt(4)*sqrt(5)=2*sqrt(5)
So if we choose the positive square root then b=5+sqrt(5) and since a=10-b then a=5-sqrt(5)
if instead we choose the negative square root then b=5-sqrt(5) and a=5+sqrt(5).
This is clear from the fact that the 2 equations are symmetrical with respect to a and b