Question

Let $a, b, c$ be distinct real numbers such that
$\Delta = \begin{vmatrix}2014 & 2015 & 2013 + a^{-1} \\\2015 & 2016 & 2013 + b^{-1} \\\2016 & 2017 & 2013 + c^{-1}\end{vmatrix} = 0$
Then:

• A. $a, b, c$ are in A.P.
• B. $a, b, c$ are in G.P.
• C. $a^2, b^2, c^2$ are in A.P.
• D. $a, b, c$ are in H.P.

Answer 1

Answer: (D)

$a, b, c$ are in H.P.

Answer 2

The correct option is (D): $a, b, c$ are in H.P.