Question

if 1/a , 1/b , 1/c are in AP prove that a(b+c) , b(c+a), c(a+b) are in AP.​

Answer 1

Answer:

Step-by-step explanation:

1

​  

,  

b

1

​  

,  

c

1

​  

 are in AP

⇒  

a

a+b+c

​  

,  

b

a+b+c

​  

,  

c

a+b+c

​  

 are in AP

⇒1+  

a b+c ,1+  b c+a  ,1+  c a+b  are in AP

⇒  b+c a+b

​  

 are in AP.

Hence proved.

Answer 2

Answer:

1/a,1/b,1/c are in AP.

Step-by-step explanation:

(b+c/a,c+a/b,a+b/c in AP)multiply by a+b+c a+b+c/a,a+b+c/b ,a+b+c/a are in AP subtract (-1) a+b+c/a -1 ,a+b+c/b -1,a+b+c/c -1 are in AP b+c/a,a+c/b,a+b/c are in AP