Olympiad Mathematics - Algebra | Poland Junior Math Olympiad Problem

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Olympiad Mathematics - Algebra | Poland Junior Math Olympiad Problem

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1. math olympiad problem
2. algebra
3. mathematical olympiad
4. olympiad mathematics

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The way I did this is rearranged a+b+c=0 to a=-b-c, then substituted -b-c for a into the equation a^2+b^2+c^2/(a^2-bc). When you expand (-b-c)^2 in that equation, it quickly simplifies to 2. You get like-terms in the numerator and denominator, the numerator terms all have coefficient 2, the terms in the denominator all have coefficient 1. You factor 2 out of the top, then then everything cancels except 2. It took 4 lines of arithmetic to simplify down to 2, it worked very nicely.

Skank_and_Gutterboy