A problem by Shivam Upadhyay

Level pending

Let \(a = |x|\) and \(b = |y|\). If \( xy > 0\), find the value of \[ \left| \dfrac{x+y}{2} - \sqrt{xy} \right| + \left| \dfrac{x+y}{2} + \sqrt{xy} \right|.\]

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