已知有理数x,y,z满足 (x-1)(x-1)+|2x-y|+|x-3z|=0 求x+y+z的值

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已知有理数x,y,z满足 (x-1)(x-1)+|2x-y|+|x-3z|=0 求x+y+z的值

已知有理数x,y,z满足 (x-1)(x-1)+|2x-y|+|x-3z|=0 求x+y+z的值
已知有理数x,y,z满足 (x-1)(x-1)+|2x-y|+|x-3z|=0 求x+y+z的值

已知有理数x,y,z满足 (x-1)(x-1)+|2x-y|+|x-3z|=0 求x+y+z的值
(x-1)(x-1)+|2x-y|+|x-3z| = 0
(x-1)^2 +|2x-y|+|x-3z| = 0
三项均为非负数,只能为0:
x - 1 = 0,x = 1
2x -y = 0,y = 2x =2
x-3z = 0,z = x/3 = 1/3
x+y+z = 1 + 2 + 1/3 =3 1/3 (三又三分之一)

根据平方数和绝对值的非负性。
X - 1 = 0
2X - Y = 0
X - 3Z = 0