Maxima and MinimaHard
Question
If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is
Options
A.2
B.1/2
C.
D.√2
Solution
Using A.M. ≥ G.M.
≥ pq
⇒ pq ≤
(p + q)2 = p2 + q2 + 2pq
⇒ p + q ≤ √2
≥ pq⇒ pq ≤
(p + q)2 = p2 + q2 + 2pq
⇒ p + q ≤ √2
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