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If a,b,c are in H.P then a/b+c, b/c+a, c/a+b will be in A.p H.p G.p None

If a,b,c are in H.P then a/b+c, b/c+a, c/a+b will be in
A.p
H.p
G.p
None

Grade:

2 Answers

Arun
25750 Points
5 years ago
Dear Anvita
 
 

Dear student,

a, b , c  are in H.P 

  we know  that  b =  2ac /  a+ c 

 now  we have to prove that  a/ b+ c ,  b / c+ a , c / a + b are in h.p 

 i .e  we  have  to prove that  b = 2ac / a+ c ---1

 

 

 

 

 

substitute value of  a+ c  from  --1  in above equation 

 

 

 

 

 

hence proved  these  are in h.p

Samyak Jain
333 Points
5 years ago
Another method : It is given that a,b,c are in H.P.
By definition, 1/a , 1/b , 1/c are in A.P.
Multiply each term by a+b+c
(a+b+c)/a , (a+b+c)/b , (a+b+c)/c  are also in A.P.
i.e. 1 + (b+c)/a , 1 + (c+a)/b , 1 + (a+b)/c  are in A.P.
Subtracting 1 from each term, we get
(b+c)/a , (c+a)/b , (a+b)/c  are in A.P.
\therefore Their reciprocals a/(b+c), b/(c+a), c/(a+b) are in H.P.

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