p+b+r=9,p/(x^2-yz)=b/(y^2-yz)=r/(z^2-xy),求(px+by+rz)/(x+y+z)的值?

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p+b+r=9,p/(x^2-yz)=b/(y^2-yz)=r/(z^2-xy),求(px+by+rz)/(x+y+z)的值?
p+b+r=9,p/(x^2-yz)=b/(y^2-yz)=r/(z^2-xy),求(px+by+rz)/(x+y+z)的值?

p+b+r=9,p/(x^2-yz)=b/(y^2-yz)=r/(z^2-xy),求(px+by+rz)/(x+y+z)的值?
p/(x^2-yz)=b/(y^2-xz)=r/(z^2-xy)=k
p=k(x^2-yz)
b=k(y^2-xz)
r=k(z^2-xy)
(px+by+rz)/(x+y+z)
=k(x^2-yz)+k(y^2-xz)+k(z^2-xy)
=p+b+r
=9

p/(x^2-yz)=b/(y^2-xz)=r/(z^2-xy)=k
p=k(x^2-yz)
b=k(y^2-xz)
r=k(z^2-xy)
(px+by+rz)/(x+y+z)
=k(x^3-xyz+y^3-xyz+z^3-xyz)/(x+y+z)
=k(x^3+y^3+z^3-3xyz)/(x+y+z)
=k(x+y+z)(x^2+y^2+z^2-xy-yz-xz)/(x+y+z)
=k(x^2+y^2+z^2-xy-yz-xz)
=k(x^2-yz)+k(y^2-xz)+k(z^2-xy)
=p+b+r
=9