Question

If a, b, c are in A.P. show that
a (b + c)/bc,b(c + a) /ca, c(a-b )/bc
are in A.P.
​

Answer 1

Explanation:

`(a(b+c))/(bc) ,(b(c+a))/(ca) ,(c(a+b))/(ab) ~are~in~A.P.\\if~(ab+ca)/(bc) ,(bc+ab)/(ca) ,(ca+bc)/(ab) ~are~in~A.P.\\add~1~to~each~term\\if~(ab+ca)/(bc) +1,(bc+ab)/(ca) +1,(ca+bc)/(ab) +1~are~in~A.P.\\if~(ab+ca+bc)/(bc) ,(bc+ab+ca)/(ca) ,(ca+bc+ab\\)/(ab) ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~(1)/(bc) ,(1)/(ca) ,(1)/(ab) ~are ~in~A.P.\\if~(a)/(abc) ,(b)/(abc) ,(c)/(abc) ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.`