Let $x, y$ be positive real numbers. Prove that $$\frac{(x+y+|x-y|)^2}{xy}\geq 4 $$$$\frac{(3x+y+|x-2y|)^2}{xy} \geq 24 $$*

Let $x, y$ be positive real numbers. Prove that $$\frac{(x+2y+|3x-4y|)^2}{xy} \geq \frac{25}{3}$$$$\frac{(5x+y+|2x-3y|)^2}{xy}\geq 48$$ sqing wrote: Let $x, y$ be positive real numbers. Prove that $$\frac{(x+y+|x-y|)^2}{xy}\geq 4 $$$$\frac{(3x+y+|x-2y|)^2}{xy} \geq 24 $$

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