If a, b, c are in A.P. show that a(b+c) /bc , b(c+a)/ca , c(a+b)/ab are in A.P.

Question

If a, b, c are in A.P. show that \(\frac{a(b+c)}{bc}\), \(\frac{b(c+a)}{ca}\), \(\frac{c(a+b)}{ab}\) are in A.P.

Answer 1

a, b, c are in A.P.

⇒ \(\frac{a}{abc}\), \(\frac{b}{abc}\) , \(\frac{c}{abc}\) are in A.P.  { Dividing each term by abc}

⇒ \(\frac{1}{bc}\), \(\frac{1}{ac}\), \(\frac{1}{ab}\) are in A.P.