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Find all the real a,b,c such that the equality
is valid for all the real x,y,z.
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If the equation holds for all
it must hold in particular forAnd for
Unfortunately, thats not good enough.
I believe there are six solutions:
Last edited by JaneFairfax (2008-10-26 05:16:27)
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Okay, try this.
First assume that
Now
means must be either all non-negative or all non-positive, i.e. either orPutting
givesNow think about it. The sum of three numbers having the same sign is ±1, and the difference between the largest and smallest of the three is 1. What does this mean? Well, it means that either
orConsidering all the possible orderings of
should yield all the six possible solutions.Last edited by JaneFairfax (2008-10-26 06:01:24)
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