Question

a/1,b/1,c/1成等差数列,证明a/b+c,b/c+a,c/a+b成等差数列

Answer 1

1/a+1/c=2/b

b=2ac/(a+c)

(b+c)/a+(a+b)/c-2(a+c)/b

=(bc(n+c)+ab(a+b)-2ac(a+c))/(abc)

=(bc+c^2+ab+a^2-(a+c)^2)/(ac)

=(2ac(a+c)/(a+c)-2ac)/(ac)=0

得证