Question

已知1/a+1/b+1/c=1/(a+b+c),求证1/a2011+1/b2011+1/c2011=1/(a2011+b

Answer 1

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

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

=(a+b)/ab+(a+b)/[c(a+b+c)]

=(a+b)[1/ab+1/c(a+b+c)]

=[(a+b)(b+c)(a+c)]/[abc(a+b+c)] = 0

所以a+b=0或b+c=0或a+c=0

所以结果成立