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Question

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=

A
ac+ca
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B
acca
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C
bq+qb
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D
bqap
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Solution

The correct option is A ac+ca
Given,
a,b,c are in A.P., p,q,r are in H.P and ap,bq,cr are in G.P
2b=a+c, q=2prp+r, (bq)2=acpr
Writing the second equation as qr=2xx+1 where x is pr
Now substituting qr in third equation and also using the first equation, we end up at a quadratic equation in x
x2(ac+ca)x+1=0
So our required problem is to find x+1x
i.e nothing but x2+1x=ac+ca

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