QJEEM07Ma2cf8: JEE Main 2007 Mathematics - Class 12 JEEM07Ma2cf8 Solution: If and are positive real numbers such that , then the maximum…

Question

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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

Accepted Answer

Given that

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

\therefore

p = \cos \theta

and

q = \sin \theta

Then

p+q

= \cos \theta + \sin \theta

We know that

- \sqrt {{a^2} + {b^2}} \le a\cos \theta + b\sin \theta \le \sqrt {{a^2} + {b^2}}

\therefore

- \sqrt 2 \le \cos \theta + \sin \theta \le \sqrt 2

Hence max. value of

p + q

is

\sqrt 2

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