已知x+y=8,xy=-5,求下列各式:(1) x²+y² (2) x²y+xy² (3) x分之y+y分之x

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已知x+y=8,xy=-5,求下列各式:(1) x²+y² (2) x²y+xy² (3) x分之y+y分之x
已知x+y=8,xy=-5,求下列各式:(1) x²+y² (2) x²y+xy² (3) x分之y+y分之x

已知x+y=8,xy=-5,求下列各式:(1) x²+y² (2) x²y+xy² (3) x分之y+y分之x
x²+y²
=(x+y)²-2xy
=8²-2*(-5)
=64+10
=74
x²y+xy²
=xy(x+y)
=8*(-5)
=-40
x分之y+y分之x
=xy分之(x²+y²)
=-5分之74

(1)=(x+y)^2-2xy=64+10=74
(2)=xy(x+y)=-40
(3)=(x^2+y^2)/xy=74/-5=-14.8

:(1) x²+y²
=(x+y)²-2xy
=64+10
=74
(2) x²y+xy²
=xy(x+y)
=-40
(3) x分之y+y分之x
=(x²+y²)/xy
=-74/5

①(x+y)^2-2xy=64+10=74
②xy(x+y)=-5*8=-40

③(x^2+y^2)/xy=-74/5

(1)(X+Y)^2-2XY=74
(2)XY(X+Y)=-40
(3)Y^2/XY+X^2/XY=X^2+Y^2/XY=-74/5