已知p+q+r=9,且px2−yz=qy2−zx=rz2−xy,则px+qy+rzx+y+z等于(  ) A.9 B.10 C.8 D.7

问题描述:

已知p+q+r=9,且

p
x2−yz
q
y2−zx
r
z2−xy
,则
px+qy+rz
x+y+z
等于(  )
A. 9
B. 10
C. 8
D. 7

设px2−yz=qy2−zx=rz2−xy=k,则p=(x2-yz)k,q=(y2-zx)k,r=(z2-xy)k.已知p+q+r=9,则(x2-yz)k+(y2-zx)k+(z2-xy)k=9,即k(x2-yz+y2-zx+z2-xy)=9.原式=k(x3+y3+z3−3xyz)x+y+z=k(x2-yz+y2-zx+z2-...