已知实数A,B,C满足A+B+C=0,ABC大于0,且X=A/|A|+B/|B|+C/|C|,Y=A(1/B+1/C)+B(1/C+1/A)+C(1/A+1/B

问题描述:

已知实数A,B,C满足A+B+C=0,ABC大于0,且X=A/|A|+B/|B|+C/|C|,Y=A(1/B+1/C)+B(1/C+1/A)+C(1/A+1/B
求X^19-96XY+Y^3

设A=2,B=-1,C=-1满足A+B+C=0,ABC>0.
X=1-1-1=-1.Y=-4+½+½=-3.
X^19-96XY+Y^3=-1-96×3-27=-316.