Question

X^2-Y^2-Z^2=0,A是一个关于X,Y,Z的一次多项式,X^3-Y^3-Z^3=(X-Y)(X-Z)A,则A的表

Answer 1

z²=x²-y²

则z³=z(x²-y²)

而y²=x²-z²

x³-y³-z³=a(x-y)(x-z)

x³-y³-z(x²-y²)=a(x-y)(x-z)

(x-y)(x²+xy+y²)-z(x-y)(x+y)=a(x-y)(x-z)

两边除以x-y

x²+xy+y²-xz-yz=a(x-z)

x²+xy+(x²-z²)-xz-yz=a(x-z)

(x²-xz)+(x²-z²)+xy-yz=a(x-z)

x(x-z)+(x+z)(x-z)+y(x-z)=a(x-z)

(x-z)(x+x-z+y)=a(x-z)

所以a=2x-z+y