Question

If a-b,b-c,c-a are in G.P then what is the relation between a,b,c.

Answer 1

The relation between the a,b,c is that the a2+b2+c2=ab+bc+ca.
a-b,b-c,c-a
t1 t2 t3
If a,b,c are in G.P then we use the formula t2/t1=t3/t2
b-c/a-b=c-a/b-c
(b-c)(b-c)=(a-b)(c-a)

By solving this we get the answer. That is a2+b2+c2=ab+bc+ca.

Answer 2

Given:

Three terms a-b,b-c,c-a are in G.P.

To Find:

The relation between a, b, and c is?

Solution:

The given problem can be solved using the concepts of Geometric progression.

1. A sequence in which every element except the first element is obtained by multiplying the preceding number with a constant ratio is defined as Geometric Progression.

2. Let x, y, and z be three consecutive terms of a geometric progression then,

=> The relation between x, y, and z is y² = x*z.

3. Using the above relation the relation between a, b, and c can be found.

=> (b-c)² = (a-b)(c-a), ( Simplify the equation )

=> b² + c²  -2bc = ac -a² - bc + ab,

=> a² + b² + c² = ac - bc + 2bc + ab,

=> a² + b² + c² = ac + bc + ab.

4. The relation between a, b, and c is a² + b² + c² = ac + bc + ab.

Therefore, the relation between a, b, and c is a² + b² + c² = ac + bc + ab.