Question

Given x, y, z are in G.P. and x^p = y^q = z^r, then 1/p, 1/q, 1/o are in
(a) A.P.
(b) G.P.
(c) Both A.P. and G.P.
(d) none of these​

Answer 1

Answer:

AP

Step-by-step explanation:

x, y and z are in GP

So,

y² = xz

Given,

x^p = y^q = z^r

x^p = y^q

So,

x = y^(q/p)

z^r = y^q

z = y^(q/r)

y² = xz

Therefore,

y² = y^(q/p) × y^(q/r)

y² = y^(q/p + q/r)

y² = y^([pq+qr]/pr)

Comparing powers,

2 = (pq+qr)/pr

pr = (pq + qr)/2

Dividing LHS and RHS by pqr,

1/q = (1/p + 1/r)/2

So,

1/p, 1/q and 1/r are in AP