已知 a2b ac2 b2c = b2a bc2 a2c，試求 (a-b)(b-c)(c-a)的值。
2005-11-18 16:23:38 · 1 個解答 · 發問者 Frank 7 in 科學 ➔ 數學
a2b + ac2 + b2c = b2a + bc2 + a2c
2005-11-18 16:29:29 · update #1
(a-b)(b-c)(c-a)
= (ab-ac-b^2+bc)(c-a)
= abc - ac^2 - b^2c + bc^2 - a^2b + a^2c - abc
= -(a^2b + ac^2 + b^2c) + (b^2a + bc^2 + a^2c)
= 0
2005-11-18 16:37:14 · answer #1 · answered by San 3 · 0⤊ 0⤋