用z(x,y)=?表示(x^2 + (9/4)y^2 + z^2 - 1)^3 - x^2z^3 - (9/80)y^2
1个回答

原式变形为(x^2+(9/4)y^2+z^2-1)^3=[x^2+(9/80)y^2]z^3

两边同时开三次方有x^2+(9/4)y^2+z^2-1=z[x^2+(9/80)y^2]^(1/3),化简有

z^2-z[x^2+(9/80)y^2]^(1/3)+[x^2+(9/4)y^2-1]=0

令P(x,y)=-[x^2+(9/80)y^2]^(1/3),Q(x,y)=x^2+(9/4)y^2-1

这是关于z的一元二次方程z^2+p(x,y)z+Q(x,y)=0,解此方程得:

z(x,y)={-P(x,y)±√[P(x,y)^2-4Q(x,y)]}/2即为结果,Δ≥0就是实数,Δ