Question

If a2,b2,c2 are in arithmetic progression prove that a/bc,b/ca,c/ab are in arithmetic progression

Answer 1

Step-by-step explanation:

1st AP:

b²-a²=c²-b².......(1)

In 2nd AP,

b/ca - a/bc = c/ab - b/ca

b²-a²/abc = c²-b²/ abc

b²-a²= c²-b²( from 1)

LHS=RHS

hence, a/bc, b/ca, c/ab,....... are in a AP.