Question

设abc不等于0,求x=a/|a|+|b|/b+c/|c|+|abc|/abc的所有值组成的集合

Answer 1

分8种情况讨论即可.

①a＞0,b＞0,c＞0,x = 4

②a＞0,b＞0,c＜0,x = 0

③a＞0,b＜0,c＞0,x = 0

④a＞0,b＜0,c＜0,x = 0

⑤a＜0,b＞0,c＞0,x = 0

⑥a＜0,b＞0,c＞0,x = 0

⑦a＜0,b＞0,c＞0,x = 0

⑧a＜0,b＞0,c＞0,x = -4

∴ x的所有值集合为{0,4,-4}