已知：a²+2b²+2c²+4=2ab+2bc+4c,求a,b,c的值

已知：a²+2b²+2c²+4=2ab+2bc+4c,求a,b,c的值
已知：a²+2b²+2c²+4=2ab+2bc+4c,求a,b,c的值

已知：a²+2b²+2c²+4=2ab+2bc+4c,求a,b,c的值
a²-2ab+b²+b²-2bc+c²+c²-4c+4 = 0
(a-b)²+(b-c)²+(c-2)² = 0
(a-b)² = 0,(b-c)²=0,(c-2)² = 0
a=b=c=2

a²+2b²+2c²+4=2ab+2bc+4c
a²+b²-2ab+b²+c²-2bc+c²-4c+4=0
(a-b)²+(b-c)²+(c-2)²=0
因为 (a-b)² >= 0 (b-c)² >= 0 (c-2)² >= 0
所以 a-b=0 b-c =0 c-2=0
a=2 b=2 c=2