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 p/r+r/p is equal to=

Answer 1

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=

a,b,c are in AP……………..a+c=2b…………………(1)

p,q,r are in HP…………….1/p +1/r= 2/q…………….(2)

ap,bq,cr are in GP…………(ap)*(cr)= b^2q^2………(3)

From 3,

ar= b^2q^2/pc

From 2

(p+r)/pr = 2/q

(a+c)/bq= 2b/bq=2/q

(a+c)/bq=(p+r)/pr

Answer 2

Answer:

Step-by-step explanation:Given *a, b, c *are in A.P.==> *2b = a + c …. (1) *Similarly *p, q, r *in H. P. ==>*q = 2pr/(p + r) …. .. .. (2) ,*and *ap, bq,cr *in G. P. ==> *(b q)^2 = ap cr …. … ..(3) . *Now from (2) & (3) we have;*b^2 q^2 = b^2 (4p^2 r^2)/(p + r)^2 = ap cr==> 4 pr/(p + r)^2 = ac/b^2 = 4ac/(a +c)^2 (from (1) ). *It *==>pr/(p+r)^2 = ac/(a+c)^2 . *Now substracting 2 from both sides , we get,*(p^2 + r^2)/pr = (a^2 + c^2)/ac or(p/r + r/p ) = (a/c + c/a)*