已知x^3-2x^2y-xy^2+2y^3=0,x>y>0,化简：xz-2yz+1.快,着急!求高人,无比感谢!

Question

已知x^3-2x^2y-xy^2+2y^3=0,x>y>0,化简：xz-2yz+1.
快,着急!求高人,无比 感谢!

Answer 1

x^3-2x^2y-xy^2+2y^3
=X^3+Y^3-2X^2Y-XY^+Y^3
=(X+Y)(X^2+Y^2-XY)-(2X^2+XY-Y^2)Y
=(X+Y)(X^2+Y^2-XY)-(X+Y)(2X-Y)Y
=(X+Y)(X-Y)(X-2Y)
而原式x^3-2x^2y-xy^2+2y^3=0
则(X+Y)(X-Y)(X-2Y)=0
又x>y>0
所以x-2y=0
xz-2yz+1
=Z（x-2y）+1
=1
明显给出的式子中没有Z这个变量,因此（XZ-2YZ）部分为常数