Question

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

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

Answer 1

Answer: (D)

$\sqrt{2}$

According to $AM\le QM$:
$\frac{a+b}{2}\le \sqrt{\frac{a^2+b^2}{2}}$ for $a,b\in R^{+}$
Equality is achieved when $a=b$.
Here:
$\frac{p+q}{2}\le \sqrt{\frac{1}{2}}$
$(p+q{)}_{\text{max}}=\sqrt{2}$