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anemone

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Assume that the quartic equation $x^4-ax^3+bx^2-ax+d=0$ has four real roots $x_1,\,x_2,\,x_3,\,x_4$ where $\dfrac{1}{2}\le x_1,\,x_2,\,x_3,\,x_4 \le 2$. Find the maximum possible value of $\dfrac{(x_1+x_2)(x_1+x_3)x_4}{(x_4+x_2)(x_4+x_3)x_1}$.

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