Strange math question

I have a math question which I'm not sure is solvable? It came from my friends correspondance math course, and it baffled me question is as follows:

Find two numbers that multiply to equal -2 and the same numbers add up to 5.

I know this isnt exactly a science/tech topic, but I figured this would be the best place to find someone with the answer. Mods feel free to move me about as required.

Thanks!

I just worked it out, and here is what I did...

Let x and y be the two numbers in question. Then, you need to find x and y so that x*y = -2 and x+y=5

Rearrange the second equation so you have y=5-x and substitute this into the first equation to get x*(5-x)=-2 Multiply it out and you get 5x-x^2=-2 If you rearrange that to get a quadratic equation you get x^2-5x-2=0 Then you can solve for x using the quadratic formula, or any other method for solving this sort of equation, and get two possibilities for x.

x = [5 + sqrt(33)]/2 = 5.372281323... (possibility 1)
x = [5 - sqrt(33)]/2 = -0.372281323... (possibility 2)

If you put x=5.37 into either one of the first two equations (xy=-2 or x+y=5) you get that y=-0.372281323, and if you put x=-0.37 into the equations, you get y=5.372281323.

So the two numbers are 5.372281323 and -0.372281323, or [5+sqrt(33)]/2 and [5-sqrt(33)]/2

edit to put in some square brackets [] to increase clarity instead of all () type brackets

another edit to say that sqrt(33) means the square root of 33

[edit on 29-1-2006 by DragonsDemesne]

[edit on 29-1-2006 by DragonsDemesne]

x=(5+ - (33) ^1/2) / 2
y=(5- + (33) ^1/2) / 2

Right...

meh, nevermind....

Does anyone know how to solve a cubic equation in the form x^3 + mx=n?

[edit on 29-1-2006 by Frosty]

Here is an online solver.

www.math.com...

When I get stumped with a problem I just use this and work backwards from the answer.

Excellent! thank you for your help everyone! Its been a while since Ive used my math skills... I should sharpen up again...

Thanks again!!!

Originally posted by Frosty
meh, nevermind....

Does anyone know how to solve a cubic equation in the form x^3 + mx=n?

[edit on 29-1-2006 by Frosty]

Rearrange it so that you get x^3 + 0x^2 + mx - n = 0

Then go to mathworld.wolfram.com... and plug in the values. WARNING: While it is only algebra, it's pretty messy. I'm sure you can do it, but I'm also sure you will be bored silly doing it. ALternately, you could use a graphing calculator to plot it, or put the function into something like Matlab.

Originally posted by sardion2000
Here is an online solver.

www.math.com...

When I get stumped with a problem I just use this and work backwards from the answer.

Hey, thats real helpful! Thank you! Great link! That will work perfect for me. I'm always getting stumped on questions, and I'm one of those types that has a hard time sleeping until I find an answer that satisfys me.

Again, Thanks so much for everybodys great help!