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"If " a^(2), b^(2), c^(2)" are in A.P., ...

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

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` (1)/(b + c),(1)/(c + a),(1)/(a+b)` are in A.P.
`rArr (1)/(c + a) - (1)/(b + c) = (1)/(a + b) - (1)/(c + a)`
`rArr (b + c - c - a)/((c + a) (b + c)) = (c + a - a- b)/((a + b)(c + a))`
`rArr (b - a)/(b + c) = (c - b)/(a + b)`
`rArr (b + a)(b - a) = (c - b) (c + b)`
`rArr a^(2) , c^(2) ` are in A.P.
Hence , if ` a^(2) , b^(2) , c^(2)` are in A. P., then ` (1)/(b + c) ,(1)/(c + a), (1)/(a + b)` are in A.P.
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