The rational number ABC is not zero, a + B + C = 0, let x = | a | - B + C + | - B | - C + A + | - C | - A + B, try to find the value of the 200 th power - 4x + 2009 of the algebraic formula X

The rational number ABC is not zero, a + B + C = 0, let x = | a | - B + C + | - B | - C + A + | - C | - A + B, try to find the value of the 200 th power - 4x + 2009 of the algebraic formula X

X=| |a|\(-a)+|b|\(-b)+|c|\(-c) |
=| |a|\a+|b|\b+|c|\c|
Because a B C is not zero, a B C may be two positive and one negative, or two negative and one positive
So x = 1
So x ^ 200-4x + 2009
=1-4+2009
=2006

Given that the rational number A.B.C is not zero, find the value of | a | / A + | B | / B + | C | / C,

For | x | / x,
When x > 0, | x | = x, | x | / x = 1
When x

If a, B, C are rational numbers, and | a + 1 | + | B + 2 | + | C + 3 | = 0, find the value of (A-1) (b-2) (C-3)

|a+1|+|b+2|+|c+3|=0
Because the absolute value > = 0, so
|a+1|=0 |b+2|=0 |c+3|=0
So a = - 1, B = - 2, C = - 3
Substituting (A-1) (b-2) (C-3) = - 2) x (- 4) x (- 6) = - 48

It is known that x is a rational number. When we find the formula │ X-1 │ + X-2 │ + x-3 │ + x-3 │ +. + X-2008 │, what is the value of X, there is the minimum value, the minimum value=

The value of X is 2008 / 2 = 1004
Minimum = 1003 + 1002 + +0+1+2+… 1004=1008016