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Old May22-09, 03:53 PM                  #1
ƒ(x)

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Posts: 137
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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Old May23-09, 12:17 AM                  #2
-Aladdin-

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Re: Tricky math problem

I'm going to ask my math teacher :)
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Old May26-09, 10:47 AM                  #3
regor60

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Posts: 73
Re: Tricky math problem

Originally Posted 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.
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Old May28-09, 04:30 PM                  #4
ƒ(x)

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Posts: 137
Re: Tricky math problem

Originally Posted 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.
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Old May29-09, 04:20 AM                  #5
-Aladdin-

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Re: Tricky math problem

How do they solve it ?
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Old Jun9-09, 02:18 PM                  #6
LAF

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Posts: 16
Re: Tricky math problem

I got the answer but i cant΄t get the values os x, y and z, but i got that x.y.z =
Spoiler
x.y.z=1
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Old Jun10-09, 12:20 PM                  #7
LAF

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Posts: 16
Re: Tricky math problem

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
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Old Jun10-09, 12:24 PM                  #8
LAF

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Posts: 16
Re: Tricky math problem

At a glance:

Spoiler
x = -y-z
x<2 and positive
y not equal z
y and z are negative
x.y.z = 1
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Old Jun10-09, 04:08 PM                  #9
LAF

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Posts: 16
Re: Tricky math problem

OK, I got it...it΄s 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


That΄s the tricky way...
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