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If a^2+2bc ,b^2+2ca, c^2+2ab are in A.P...

If ` a^2+2bc ,b^2+2ca, c^2+2ab` are in A.P. then :-

Text Solution

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`b^2+2ca-a^2-2bc=c^2+2ab-b^2-2ca`
`(b+a)(b-a)+2c(a-b)=(c+b)(c-b)+2a(b-c)`
`(a-b)[2c-a-b]=(b-c)[2a-c-b]`
`(a-b)[(c-a)+(c-b)]=(b-c)[(a-c)+(a-b)]`
`(a-b)(c-a)+(a-b)(c-b)=(b-c)(a-c)+(b-c)(a-b)`
`(a-b)(c-a)-(a-b)(b-c)=-(b-c)(c-a)+(b-c)(a-b)`
divide by (a-b)(b-c)(c-a)
`1/(b-c)-1/(c-a)=-1/(a-b)+1/(c-a)`
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