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
ac−ca
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C
bq+qb
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D
bq−ap
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Solution
The correct option is Aac+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