數學 : 求值

1) a2 - b2 = bc - ca

(a - b)(a + b) = c(b - a)

a + b = -c

a + b + c = 0

b) (1/a + 1/b + 1/c)a2011

= a2010 + a2011 (b + c)/(bc)

= a2010 + a2011 (-a)/a2

= a2010 - a2010

= 0

(1/a + 1/b + 1/c)b8

= b7 + b8 (a + c)/(ac)

= b7 - b8 (-b)/b2

= b7 - b7

= 0

(1/a + 1/b + 1/c)c7

= c6 + c7 (a + b)/(ab)

= c6 - c7 (-c)/c2

= c6 - c6

= 0

所以, (1/a + 1/b + 1/c)(a2011 + b8 + c7) = 0

2011-08-07 14:48:01 補充：
c^2 = ab 的證明:

a^2 = bc
b^2 = ac

a^2 b^2 = abc^2

ab = c^2