A) \[3ad\]
B) \[(a+b)(c+d)\]
C) \[3ac\]
D) None of these
Correct Answer: A
Solution :
Since \[a,\ b,\ c,\ d\] are in H.P., therefore \[b\]is the H.M. of \[a\] and \[c\] \[i.e.\] \[b=\frac{2ac}{a+c}\] and \[c\] is the H.M. of \[b\] and \[d\] \[i.e.\]\[c=\frac{2bd}{b+d}\], \[\therefore \] \[(a+c)(b+d)=\frac{2ac}{b}.\frac{2bd}{c}\] \[\Rightarrow \]\[ab+ad+bc+cd=4ad\]\[\Rightarrow \]\[ab+bc+cd=3ad\]. Trick: Check for\[a=1,\ b=\frac{1}{2},\ c=\frac{1}{3},\ d=\frac{1}{4}\].
You need to login to perform this action.
You will be redirected in
3 sec
