Question
Let $a, b, c$ be distinct real numbers which are in G.P. If $x \in \mathbf{R}$ is such that $a+x, b+x, c+x$ are in H.P.s then $x$ equals(a) $a$(b) $b$(c) $c$(d) $(a+b+c) / 3$
Step 1
P., we have $b^2 = ac$. Also, given that $a+x, b+x, c+x$ are in H.P., we have $\frac{1}{b+x} = \frac{1}{2} \left( \frac{1}{a+x} + \frac{1}{c+x} \right)$. Show more…
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