FANDOM

Assume that the quartic $x^4-ax^3+bx^2-ax+d=0$ has four real roots $\tfrac{1}{2} \leq x_1, x_2, x_3, x_4 \geq 2$. Find the maximum possible value of $\tfrac{(x_1+x_2)(x_1+x_3)x_4}{(x_4+x_2)(x_4+x_3)x_1}$ over all possible values of $a,b,d$.