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.

∵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=
2
3
+1+2=
11
3