## {x+y, x+z, y+z} are all squares, and 2(x+y+z) a biquadrate

Find three positive integers   $x, \; y, \; z$   the sum of any two of which is a square:

$x \; + \; y \; = \; a^2$
$x \; + \; z \; = \; b^2$
$y \; + \; z \; = \; c^2$

and double the sum of all three is a biquadrate:

$2 \,(x + y + z) \; = \; d^4$