A) \[{{a}^{2}}b,\,{{c}^{2}}a,\,{{b}^{2}}c\] 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.
D) None of these
Correct Answer: A
Solution :
\[\frac{b}{a},\frac{c}{b},\frac{a}{c}\] are in A.P. Þ \[\frac{2c}{b}=\frac{b}{a}+\frac{a}{c}\]\[\Rightarrow \frac{2c}{b}=\frac{bc+{{a}^{2}}}{ac}\] Þ \[2a{{c}^{2}}={{b}^{2}}c+b{{a}^{2}}\] \[\therefore \,{{a}^{2}}b,\,{{c}^{2}}a\] and \[{{b}^{2}}c\]are in A.P.
You need to login to perform this action.
You will be redirected in
3 sec
