Question

若a+b+c=0,求a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)的值

写一下过程,谢谢~`~

Answer 1

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

= c/b + a/b + a/c + b/c + b/a + c/a

= a+c/b + a+b/c + b+c/a

因为a+b=-c a+c=-b b+c=-a

原式(-1)+ (-1) + (-1)
=-3

Answer 2

a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
= c/b + a/b + a/c + b/c + b/a + c/a
= a+c/b + a+b/c + b+c/a
因为a+b=-c a+c=-b b+c=-a
原式(-1)+ (-1) + (-1)
=-3

Answer 3

将a=2, b=-1, c=-1带入可得答案为-3