Divide a positive number, say 20, into a sum of two positive rational numbers x, y such that for some positive rational number z both z 2 + x and z 2 + y are squares (of rational numbers). For the...

Divide a positive number, say 20, into a sum of two positive rational numbers x, y such that for some positive rational number z both z²
+ x and z²
+ y are squares (of rational numbers). For the sake of definiteness, write z²
+ x = (z+2)²
and z²
+ y = (z + 3)².