若9m2-12mn+8n2-4np+2p2-4p+4=0,求m+n+p的值.
问题描述:
若9m2-12mn+8n2-4np+2p2-4p+4=0,求m+n+p的值.
答
∵9m2-12mn+8n2-4np+2p2-4p+4
=(9m2-12mn+4n2)+(4n2-4np+p2)+(p2-4p+4)
=(3m-2n)2+(2n-p)2+(p-2)2=0,
可得:
,
3m-2n=0 2n-p=0 p-2=0.
解得:
,
m=
2 3 n=1 p=2.
则m+n+p=
+1+2=2 3
.11 3