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Tricky math problem

 
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May22-09, 02:53 PM   #1
 

Tricky math problem

A friend of mine showed this to me a few days ago:

x+y+z=0
x3+y3+z3=3
x5+y5+z5=15

x2+y2+z2=?

An answer must be supported with justification (so that I know that you didn't guess and get lucky).
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May22-09, 11:17 PM   #2
 
I'm going to ask my math teacher :)
May26-09, 09:47 AM   #3
 
Quote by ƒ(x) View Post
A friend of mine showed this to me a few days ago:

x+y+z=0
x3+y3+z3=3
x5+y5+z5=15

x2+y2+z2=?

An answer must be supported with justification (so that I know that you didn't guess and get lucky).

Unless you can demonstrate that there is a clever shortcut to this problem which would raise it to the level of a brainteaser, this is just a set of simultaneous equations which is easily solvable with, for example, the Wolfram Alpha website.
May28-09, 03:30 PM   #4
 

Tricky math problem

Quote by regor60 View Post
Unless you can demonstrate that there is a clever shortcut to this problem which would raise it to the level of a brainteaser, this is just a set of simultaneous equations which is easily solvable with, for example, the Wolfram Alpha website.
I had no idea that such a site even existed.
May29-09, 03:20 AM   #5
 
How do they solve it ?
Jun9-09, 01:18 PM   #6
LAF
 
I got the answer but i cantīt get the values os x, y and z, but i got that x.y.z =
Spoiler
x.y.z=1
Jun10-09, 11:20 AM   #7
LAF
 
Ok...that was prety hard to solve...it took many hours. I hope you have an easier way to get the answer (tricky):
Spoiler
x= 2 cos (20)
y= 2 cos (140)
z= 2 cos (260)
the answer to the question is 6
Jun10-09, 11:24 AM   #8
LAF
 
At a glance:

Spoiler
x = -y-z
x<2 and positive
y not equal z
y and z are negative
x.y.z = 1
Jun10-09, 03:08 PM   #9
LAF
 
OK, I got it...itīs really simple to get the answer to x2+y2+z2=?....
Spoiler
the answer is 6. and you just have to set values to x (positive) y(negative) and z(negative) and calcutale the proportion like: set x=3 y=-2 z=-1, then
^2 = 14 --> ?
^3 = 18 --> 3
^5 = 210 --> 15

so 14 . 18 . 15 = ? . 3 . 210
? = 6


Thatīs the tricky way...
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