Let w=1/x+1/y+1/z. Then the given condition is w^3=w. So w=0 or 1 or -1. Since xyz>0, we have w>0. Hence w=1. This completes the proof.
求教初二数学难题已知：(1/x+1/y+1/z)^(1/3)=1/x+1/y+1/z,且xyz>0,求证：1/x+1/y
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