A Nice Math Olympiad Algebra Problem | You should learn this trick?

A Nice Math Olympiad Algebra Problem | You should learn this trick?
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Substitute y=1/x and rearrange to y^3-y^2+80=0. By inspection y=-4 and x=1/y=1/(-4)=-1/4. Divide by (y+4): y^2-5y+20=0; y=(5±i√55)/2 & x=1/y=-2/(5±i√55)=-2(5±i√55)/80=(±i√55-5)/40