If a,b,c are in H.P., then the expression E=`(1/b+1/c-1/c)(1/c+1/a-1/b)` equals

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If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c. If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c.
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