Question

Let x and y be two varibles such that $x>0$ and $xy=1$. Find the minimum value of $x+y$.

• A. $2$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $1$

Answer 1

The correct option is A $2$

Let, $z=x+y=x+\frac{1}{x}$
for minimum value of $z$
$\frac{dz}{dx}=0\Rightarrow 1-\frac{1}{x^2}=0\Rightarrow x=\pm 1$
but given $x>0,\Rightarrow x=1$
Hence minimum value of $z$ is 2.