I have the following three functions
$f_1(x) = \frac{1}{4} (8-3x + \sqrt{(x-2) (5x-14)}) (1-x)$
$f_2(x) = \frac{1}{8} (12-4x + \sqrt{2} \sqrt{(5x-14)(x-3)} + \sqrt{2} \sqrt{(x-2)(x-3)} )(1-x)$
$f_3(x) = (x-1)(x-2)$
How possible can it be shown that
$f_1(x) > (or <) f_2(x) < (or >) f_3(x)$