AM-GM Inequality!

Algebra Level 3

True or False

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

xy+1xy2xy(1xy)=2\large xy+\frac{1}{xy}\ge2\sqrt{xy\left(\frac{1}{xy}\right)}=2

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

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