Question

If a2, b2, c2 are in A. P. Then prove that b + C,c + a, a + b are in H. P.​

Answer 1

Answer:

Given : a

2

,b

2

,c

2

are in A.P

By adding ab+ac+bc to each term, we see that

a

2

+ab+ac+bc,b

2

+ba+bc+ac,c

2

+ca+cb+ab are in A.P.;

That is (a+b)(a+c),(b+c)(b+a),(c+a)(c+b) are in A.P.

∴ Dividing each term by (a+b)(b+c)(c+a),

b+c

1

,

c+a

1

,

a+b

1

are in A.P.;

That is, b+c,c+a,a+b are in H.P.