AM-GM Inequality!

Algebra Level 4

True or False

Positive real numbers \(x\) and \(y\) are such that \(x+y < 2\). By AM-GM inequality, we have:

\[\large xy+\frac{1}{xy}\ge2\sqrt{xy\left(\frac{1}{xy}\right)}=2\]

Then is it true that \(xy+\dfrac{1}{xy}\) has a minimum value of 2?

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