1.
(a+b-2c)^2
=a²+b²+(-2c)²+2ab+2a(-2c)+2b(-2c)
=a²+b²+4c²+2ab-4ac-4bc
2.
a²+2b²+2c²+4=2ab+2bc+4c
a²-2ab+b²+b²-2bc+c²+c²-4c+4=0
(a-b)²+(b-c)²+(c-2)²=0
∴a-b=0,b-c=0,c-2=0
∴a=b=c=2
若 非负数a+非负数b+非负数c=0
则a=0,b=0,c=0
1.
(a+b-2c)^2
=a²+b²+(-2c)²+2ab+2a(-2c)+2b(-2c)
=a²+b²+4c²+2ab-4ac-4bc
2.
a²+2b²+2c²+4=2ab+2bc+4c
a²-2ab+b²+b²-2bc+c²+c²-4c+4=0
(a-b)²+(b-c)²+(c-2)²=0
∴a-b=0,b-c=0,c-2=0
∴a=b=c=2
若 非负数a+非负数b+非负数c=0
则a=0,b=0,c=0