Question

已知a^2+b^2+c^2=(a+b+c)^2且abc≠0,求1/a+1/b+1/c的值

Answer 1

(a+b+c)^2

=(a+b)^2+2c(a+b)+c^2

=a^2+2ab+b^2+2ac+2bc+c^2

＝a^2+b^2+c^2+2ab+2bc+2ac

=a^2+b^2+c^2

所以2ab+2bc+2ac=0

ab+bc+ac=0

所以1/a+1/b+1/c

=(bc+ac+ab/)abc

=0