if a,b,c are in H.P. then prove that a/(b+c), b/(a+c), c/(a+b) are in H.P. Please give me complete ans with steps. Thanks in advance.

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

(b+c)/a,(a+c)/b,(a+b)/c will be in a.p.

so (b+c)/a+1,(a+c)/b+1,(a+b)/c+1 also in a.p

=(a+b+c)/a,(a+b+c)/b,(a+b+c)/c

so1/a,1/b,1/c will be in ap

so a,b,c will be in h.p