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- Feb 14, 2012

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Problem:

Solve for reals of

$m-n-s+t=1$

$m^2+n^2-s^2-t^2=3$

$m^3-n^3-s^3+t^3=-5$

$m^4+n^4-s^4-t^4=15$

I've encountered this problem a while back and I've tried to use many methods (which include by manipulating some inequality theorems or solving them by the elimination of variables method or trying to relate the second equation and the third by multiplying the second and the third (after changing the minus sign) and let it equal to the 4th equation but all these methods have fallen apart. I am getting very tired of it and hence I hope someone could help me by giving me some hints so that I can finish the unfinished problem.

Thanks.