Let be positive real numbers such that .

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

p,\,q,\,r

be positive real numbers such that

pqr = 64

. (i) Establish that the sum

S = p + q + r

is bounded below. (ii) Prove that the minimum value of

S

is achieved when

p = q = r

. (iii) Find the minimum value of

S

and the common value of

p,\,q,\,r

at which it occurs.