Sequence And Series Question 282
Question: If $ G_1 $ and $ G_2 $ are two geometric means and A the arithmetic mean inserted between two numbers, then the value of $ \frac{G_1^{2}}{G_2}+\frac{G_2^{2}}{G_1} $ is
[DCE 1999]
Options:
A) $ \frac{A}{2} $
B) A
C) 2 A
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let the two numbers be p and q.
$ \therefore G_1={p^{2/3}}{q^{1/3}},G_2={p^{1/3}},{q^{2/3}} $
$ \therefore ,\frac{G_1^{2}}{G_2}+\frac{G_2^{2}}{G_1}=\frac{{p^{4/3}}{q^{2/3}}}{{p^{1/3}}{q^{2/3}}}+\frac{{p^{2/3}},{q^{4/3}}}{{p^{2/3}},{q^{1/3}}} $ $ =p+q=2\times ,( \frac{p+q}{2} ),=2A $ .
BETA
