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  • If a,b,c are in A.P p,q,r are in H.P and ap,bq,cr are in G.P then p/r+r/p is equal to

If a,b,c are in A.P p,q,r are in H.P and ap,bq,cr are in G.P then p/r+r/p is equal to

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Solution: According the given condition

2b=a+c,q=2pr/p+r ;and;(bq)^2=(ap)(cr)

Substituting value of b and q from First two expression

in the last expression ,we get

(a+c)^2/4 imes (2pr/p+r)^2=(ac)(pr)\ \Rightarrow (a+c)^2/ac=(p+r)^2/prRightarrow a/c+c/a=p/r+r/p

Posted by

Deependra Verma

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