Question : The mean proportional of $a$ and $b$ is $c$. What is the mean proportion of $a^2c$ and $b^2c$?
Option 1: $c$
Option 2: 3$c$
Option 3: $c^3$
Option 4: $c^2$
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Correct Answer: $c^3$
Solution :
$c^2 = ab$
where c is the mean proportion of a and b
Now, the mean proportion of $a^2c$ and $b^2c$
= $\sqrt{b^2c \times a^2c}$
= $a.b.c$
= $c^2 \times c$
= $c^3$
Hence, the correct answer is $c^3$.
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