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-   -   Math Riddle | 17 Jul 2009 (http://www.go4expert.com/contests/math-riddle-17-jul-2009-t18592/)

 shabbir 17Jul2009 21:47

Math Riddle | 17 Jul 2009

A bit tricky and interesting as well

x+y+z=0
x^3+y^3+z^3=3
x^5+y^5+z^5=15

x^2+y^2+z^2=?

^ = Power of

 rik625 18Jul2009 04:36

Re: Math Riddle | 17 Jul 2009

Hey...

x^2+y^2+z^2 =1

Im i right???

 xpi0t0s 18Jul2009 05:42

Re: Math Riddle | 17 Jul 2009

It'd better not be as simple as that...after several hours and sheets of paper I'm just about to give up on solving it with simultaneous equations...

 xpi0t0s 18Jul2009 06:15

Re: Math Riddle | 17 Jul 2009

However that did give me a useful inequality...so I'm going to register a guess, that x^2+y^2+z^2 is an integer and is precisely 6. Just running another, more accurate, test but it'll take a while to produce results.

 shabbir 18Jul2009 07:19

Re: Math Riddle | 17 Jul 2009

Quote:
 Originally Posted by xpi0t0s (Post 52895) However that did give me a useful inequality...so I'm going to register a guess, that x^2+y^2+z^2 is an integer and is precisely 6. Just running another, more accurate, test but it'll take a while to produce results.
Yes that is the right Answer :D

I have the values of x,y,z as well if you want to.

 naimish 18Jul2009 07:48

Re: Math Riddle | 17 Jul 2009

@ xpi0t0s, Congrs Buddy :)

Re: Math Riddle | 17 Jul 2009

Of course X^2+y^2+z^2 can be real even if x, y, z are all complex. But, I'm just curious .. Do these equations have any real solutions ?? :crazy:

Re: Math Riddle | 17 Jul 2009

I wonder why I keep getting 60 as the answer. :(

 shabbir 18Jul2009 13:02

Re: Math Riddle | 17 Jul 2009

The answer is 6 and X=3, y=-2 and Z=-1