问题
填空题
已知
|
答案
∵
=3 x+y
=4 y+z
，5 z+x
∴
⇒
=3 x+y 4 y+z
=3 x+y 5 z+x
=4 y+z 5 z+x
⇒
=y+z 4 x+y 3
=x+z 5 x+y 3
=x+z 5 y+z 4
=x+y 3
=y+z 4 x+z 5
∴令
=x+y 3
=y+z 4
=ax+z 5
则有 x+y=3a ① y+z=4a ② x+z=5a ③
由①+②+③得 x+y+z=6a ④
由④-①得 z=3a，
同理解得x=2a，y=a
∴
=x2+y2+z2 xy+yz+zx
=(22+12+32)a2 (2×1+1×3+2×3)a2 14 11
故答案为
．14 11