Math miscellaneousHard

Question

If a,b and c are in H.P and a,b and - 2c are in G.P., where a,b & c are non-zero, then -

Options

A.-2a,b and -2c are in A.P
B. = 0
C.- 2a,b and - 2c are in G.P
D. = (a + b + c)2

Solution

b = and b2 = - 2ac
⇒ b = ⇒ a + b + c = 0

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