If `(b-c)^2,(c-a)^2,(a-b)^2` are in A.P. prove that `1/(b-c),1/(c-a),1/(a-b),` are in A.P.

Explanation

`(b - c)^(2) , (c -a)^(2) , (a -b)^(2) ` are in A.P.
Subtract ` a^(2) + b^(2) + c^(2) ` and multiply by (-1) ,
`rArr a^(2) + 2bc , b^(2) + 2ca, a^(2) + 2ab ` are in A.P.
Subtract ` ab + bc + ca `
` rArr (a - b) (a - c) , (b - c) (b - a) , (c -a) (c-b)` are in A.P.
Divide by `(a -b)( , (b -c),(c -a)`
` rArr (-1)/(b-c) , (-1)/(c-a), (-1)/(a-b) ` are in A.P.