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

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Aicharya · Accepted Answer

Using $A.M.$ $\geq$ $G.M.$ $\begin{aligned} & \frac{p^2+q^2}{2} \geq p q \ & \Rightarrow p q \leq \frac{1}{2} \ & (p+q)^2=p^2+q^2+2 p q \ & \Rightarrow p+q \leq \sqrt{2} . \end{aligned}$

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

Solution