if a,b,c are in A.P p,q,r are in H.P and ap,bq,cr are in G.P THEN PR+RP IS
(1) AC-CA
(2) AC+CA
(3) BQ+QB
(4) BQ-QB
62preeti.. is it PR + RP??
Bcos then you could as well have aksed 2PR!!??
1if its objective , i can help :)
take a=b=c=1, p=q=r=1.
then ap=bq=cr=1
then for p/r+r/p = 2 , we can eliminate options 1 and 4.
since they will give 0.
now take some suitable value : a=1,b=2,c=3
p=1,q=1/2 , r=1/3
then ap=1, bq=1, cr=1
for these values we have, p/r+r/p=3+1/3
so clearly the same value is given by c/a+a/c.
hence opton (a) is correct .. :)
is 'a' correct b/w (90% sure :P) ;)
1we have
b2q2=acpr ...(1)
2b=a+c ........(2)
2/q=(p+r)/pr ......(3)
substitute b and q from (2) and (3) and put it in (1)
(a+c)2/4 * 4p2r2/(p+r)2=acpr
or
(p+r)2/pr=(a+c)2/ac
or p/r+r/p=a/c+c/a
1yiipppeeeeee!! i was correct :) though it was not 'maths'.. but still .. ;)