Question

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

• A. $2$
• B. $1/2$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

Using $A.M.\ge G.M.$
$\frac{p^2+q^2}{2}\ge pq$
$\Rightarrow pq\le \frac{1}{2}$
${\left(p+q\right)}^2=p^2+q^2+2pq$
${\left(p+q\right)}^2=p^2+q^2+2pq$
$\Rightarrow p+q\le \sqrt{2}.$