(1) \(2r\sqrt {pq} \)
(2) \(2pq\sqrt 3 \)
(3) \( - 2r\sqrt {pq} \)
(4) \(\sqrt {pqr} \)
[NIMCET 2011]
Solution: Given that \(p,q,x,y\) are positive numbers, we can apply \(AM \ge GM\)
\(\left( {\frac{{px + qy}}{2}} \right) \ge \sqrt {(px \times qy)} \)
\( \Rightarrow px + qy \ge 2\sqrt {pqxy} \)
Given that \(xy = {r^2}\), hence minimum value of \(px + qy\) is \(2r\sqrt {pq} \)