Quadratic Equations · Equations reducible to quadratic with modulus

\alpha

and

\beta

(\alpha < \beta)

are the roots of the equation

\left(-2 + \sqrt3\right)\left(\left\lvert\sqrt x - 3\right\rvert\right) + \left(x - 6\sqrt x\right) + \left(9 - 2\sqrt3\right) = 0,

x \ge 0

, then

\sqrt{\dfrac{\beta}{\alpha}} + \sqrt{\alpha\beta}

is equal to:

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