Question

已知a.b.c均为有理数,且a(1/b+1/c)+b(1/c/a)+c(1/a+1/b)=3 而且a+b+c不等于0,求

Answer 1

(1/c/a)是否写错了

a(1/b+1/c)+b(1/c/a)+c(1/a+1/b)=3,

a/b+a/c+b/c+b/a+c/a+c/b=3,

(b+c)/a+(a+c)/b+(a+b)/c=3,

(b+c)/a+1+(a+c)/b+1+(a+b)/c+1=6,

(a+b+c)/a+(a+b+c)/b+(a+b+c)/c=6,

1/a+1/b+1/c=6/(a+b+c)