If p and q are positive real numbers such that p^2+q^2=1, then the maximum value of (p+q) …

Question

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 $$\sqrt 2 $$

Solutions · 1