MCQ
If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then
- ✓${a^2}b,\,{c^2}a,\,{b^2}c$ are in $A.P.$
- B${a^2}b,\,{b^2}c,\,{c^2}a$ are in $H.P.$
- C${a^2}b,\,{b^2}c,\,{c^2}a$ are in $G.P.$
- DNone of these
==> $\frac{{2c}}{b} = \frac{b}{a} + \frac{a}{c}$
$ \Rightarrow \frac{{2c}}{b} = \frac{{bc + {a^2}}}{{ac}}$
==> $2a{c^2} = {b^2}c + b{a^2}$
$\therefore \,{a^2}b,\,{c^2}a$ and ${b^2}c$ are in $A.P.$
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