若有理数x.y.z满足等式(x-2)*(x-2)+(2x-y)*(2x-y)*(2x-y)*(2x-y)*+|x-3z|=0,求x+y+z的值
问题描述：
若有理数x.y.z满足等式(x-2)*(x-2)+(2x-y)*(2x-y)*(2x-y)*(2x-y)*+|x-3z|=0,求x+y+z的值
答
(x-2)*(x-2)+(2x-y)*(2x-y)*(2x-y)*(2x-y)*+|x-3z|=0
=>
(x-2)^2+(2x-y)^4+|x-3z|=0
偶数次方和绝对值的值恒为非负值，三者和为0，说明他们都为0
所以
x-2=0,2x-y=0,x-3z=0
=>
x=2,y=4,z=2/3
所以
x+y+z=2+4+2/3=20/3
答
(x-2)*(x-2)+(2x-y)*(2x-y)*(2x-y)*(2x-y)+|x-3z|=0
x-2=0
2x-y=0
x-3z=0
x=2
y=4
z=2/3
x+y+z=20/3