Problem 36

Algebra Level 5

\[\large \dfrac{\left(\frac{a}{b}+\frac{b}{a}+1\right)\left(\frac{1}{a}-\frac{1}{b}\right)^2}{\frac{a^2}{b^2}+\frac{b^2}{a^2}-\left(\frac{a}{b}+\frac{b}{a}\right)}\]

Given that \(a\) and \(b\) are distinct positive reals satisfying \(4a+b+\sqrt{ab}=1\).

Find the minimum value of the expression above.


See my set of inequality problems.
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