已知x=6-y,z2=9-xy,z≠3-y,則x+2y-z= .
【答案】分析:先將x=6-y代入z2=9-xy=(y-3)2,解得:z=y-3或z=3-y,再根據z≠3-y,得到z=y-3,代入原式x+2y-z=6-y+2y-y+3=9.
解答:解:∵x=6-y
∴z2=9-xy
=9-(6-y)y
=9-(6y-y2)
=y2-6y+9
=(y-3)2
∴z=y-3或z=3-y
∵z≠3-y
∴z=y-3
∴x+2y-z=6-y+2y-y+3=9
故答案為9.
點評:本題考查了配方法的解法,解題的關鍵是代入后正確的變形為完全平方的形式.