Find the mean proportional for each of the following:
(i) $9, 25$

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Solution

Calculate the mean proportional:
Let $x$ be the mean proportion.
If $x$ is the mean proportional of $a$ and $b$ , then $a : x : : x : b$ .
Since, $x$ is the mean proportional, therefore, $9 : x : : x : 25$ .
$\Rightarrow 9 : x = x : 25 (C h a n g i n g t h e p r o p o r t i o n a l i t y s i g n t o e q u a l s i g n) \Rightarrow \frac{9}{x} = \frac{x}{25} \Rightarrow 9 \cdot 25 = x \cdot x (C r o s s m u l t i p l y i n g b o t h s i d e s) \Rightarrow x^{2} = 225 ∴ x = \pm 15 (T a k i n g s q u a r e r o o t o n b o t h s i d e s)$
Since $- 15$ does not lie between 9 and 25, therefore, the mean proportional is $15 .$
Final Answer: The mean proportional is $15$ .

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