Question

If b+c, c+a, a+b are in A.P then a, b, c are in
a) A.P
b) G.P
c) H.P
d) A.G.P​

Answer 1

Answer:

a) A.P

Step-by-step explanation:

If a,b,c are in AP

a+c=2b

we need to prove a+b,c+a,b+c are in AP

∴2(a+c)=b+c+a+b

2c+2a=2b+c+a

a+c=2b

∴proved.

Answer 2

Answer:

hey mate !! here is your answer..

Step-by-step explanation:

Given:a

2

,b

2

,c

2

are in A.P

∴b

2

−a

2

=c

2

−b

2

⇒(b−a)(b+a)=(c−b)(c+b)

⇒(b+c−c−a)(b+a)=(c+a−a−b)(c+b)

⇒[(b+c)−(c+a)](b+a)=[(c+a)−(a+b)](c+b)

⇒(a+b)(b+c)−(a+b)(c+a)=(b+c)(c+a)−(b+c)(a+b)

Dividing both sides by (a+b)(b+c)(c+a) we get

c+a

1

−

b+c

1

=

a+b

1

−

c+a

1

⇒

b+c

1

,

c+a

1

,

a+b

1

are in A.P