AP-GP-HP
Algebra
Level
3
If a,b,c are in AP , p,q,r are in HP and ap,bq,cr are in GP.
Then the value of p/r + r/p is:
a/c - c/a
a/c + c/a
b/q + q/b
b/q - q/b
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1 solution
p/r +r/p = \frac{p+r^2}{pr} =S+2 { S is the value of expression which we've to find}
2/q * 2/q=(p+r)^2/pr*pr
that is 4 pr/q q =(p+r)^2/pr
#4 pr/q q =S+2
4 pr b^2 q^2/apcr q q=S+2 as b b q q=apcr
4b*b/ac -2=S
therefore ( a+ c )^2/ac -2 =S
S=a/c + c/a