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If p and q are positive real numbers such that p^{2} + q^{2} =

Question

If p and q are positive real numbers such that $p^{2} + q^{2} = 1$ , then the maximum value of (p + q) is-

\frac{1}{2}

\frac{1}{2}

2

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If p and q are positive real numbers such that

p^{2} + q^{2} = 1

, then the maximum value of (p + q) is-

10 mins ago

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10 mins ago

Text solutionVerified

Using

A M \geq GM

p

and

q

\frac{p ^{2} + q ^{2}}{2} \geq pq

\Rightarrow pq \leq \frac{1}{2} (∵ p^{2} + q^{2} = 1)

Now,

(p + q)^{2} = p^{2} + q^{2} + 2 pq

\Rightarrow (p + q)^{2} = 1 + 2 pq

\Rightarrow (p + q)^{2} \leq 1 + 1

\Rightarrow p + q \leq 2

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Question Text	If p and q are positive real numbers such that $p^{2} + q^{2} = 1$ , then the maximum value of (p + q) is-
Answer Type	Text solution:1
Upvotes	150