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Question

If a,b,c are in A.P., then show that,
(a+2bc)(2b+ca)(c+ab)=4abc

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Solution

If a, b, c are in AP then 2b=a+c
(a+2bc)(2b+ca)(c+ab)
(a+a+cc)(c+a+ca)(2bb)
(2a)(2c)(b)
4abc

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