數學知識交流---解不定方程(2)

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2011-09-13 22:35:26 補充：
The above table is constructed as follows:

Consider the first factor x-1:
When x<1 x is negative
When 1<2 or 2<3 or 3<4 or 4<5 or x>5 x is positive

Consider the second factor x-2:
When x<1 or 1<2 x is negative
When 2<3 or 3<4 or 4<5 or x>5 x is positive

2011-09-13 22:35:42 補充：
The result is obtained as follows:

When x<1
x-1, x-2, x-3, x-4 and x-5 are negative
(x-1)(x-2)(x-3)(x-4)(x-5) is negative

When 1<2
x-1 is positive
x-2, x-3, x-4 and x-5 are negative
(x-1)(x-2)(x-3)(x-4)(x-5) is positive

2011-09-13 22:36:53 補充：
Some typing mistake:

When 1<2
x-1 is positive
x-2, x-3, x-4 and x-5 are negative
(x-1)(x-2)(x-3)(x-4)(x-5) is positive

2011-09-13 22:39:46 補充：
"x" are missing:

Consider the first factor x-1:
When x < 1 x is negative
When 1 < x < 2 or 2 < x < 3 or 3 < x < 4 or 4 < x < 5 or x > 5 x is positive

Consider the second factor x-2:
When x < 1 or 1 < x < 2 x is negative
When 2 < x < 3 or 3 < x < 4 or 4 < x < 5 or x > 5 x is positive

2011-09-13 22:40:48 補充：
When x < 1
x-1, x-2, x-3, x-4 and x-5 are negative
(x-1)(x-2)(x-3)(x-4)(x-5) is negative

When 1 < x < 2
x-1 is positive
x-2, x-3, x-4 and x-5 are negative
(x-1)(x-2)(x-3)(x-4)(x-5) is positive

2011-09-13 23:17:13 補充：
I am sorry that I make too many mistakes:

Consider the first factor x-1:
When x < 1, x-1 is negative
When 1 < x < 2 or 2 < x < 3 or 3 < x < 4 or 4 < x < 5 or x > 5, x-1 is positive

2011-09-13 23:17:25 補充：
Consider the second factor x-2:
When x < 1 or 1 < x < 2, x-2 is negative
When 2 < x < 3 or 3 < x < 4 or 4 < x < 5 or x > 5, x-2 is positive

1) 解不定方程 (x-)(x-2)(x-3)(x-4)(x-5) ≧ 0
(2) 解不定方程 (x-1)(x-2)(x-3)(x-4)(x-5) ≦ 0

(1) x≧1或2或3或4或5
(2) x≦1或2或3或4或5