Sequence And Series Question 575
Question: If $ a,,b,,c $ are in G.P., then
Options:
A) $ a(b^{2}+a^{2})=c(b^{2}+c^{2}) $
B) $ a(b^{2}+c^{2})=c(a^{2}+b^{2}) $
C) $ a^{2}(b+c)=c^{2}(a+b) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
If $ a,\ b,\ c $ are in G.P. Then $ b^{2}=ac $
$ \Rightarrow $ $ b^{2}(a-c)=ac(a-c) $
$ \Rightarrow $ $ b^{2}a-b^{2}c=a^{2}c-ac^{2} $
$ \Rightarrow $ $ a(b^{2}+c^{2})=c(a^{2}+b^{2}) $ . Trick: Put $ a=1,\ b=2,\ c=4 $ and check the alternates.
BETA
