(2为平方,/为分数线）已知p+q+r=9,且p/x2-yz=q/y2-xz=r/z2-xy,则px+qy+rz/x+y+z等于（）A.9B.10C.8D.7

Question

(2为平方,/为分数线）
已知p+q+r=9,且p/x2-yz=q/y2-xz=r/z2-xy,则px+qy+rz/x+y+z等于（ ）
A.9 B.10 C.8 D.7

Answer 1

应该选A.
设p/(x^2-yz)=q/(y^2-xz)=r/(z^2-xy)=k,
则p=k(x^2-yz),q=k(y^2-xz),r=k(z^2-xy) ,代入整理可得
(px+qy+rz)/(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-xz-yz)/(x+y+z)
=k(x^2+y^2+z^2-xy-xz-yz)
=p+q+r
=9