## To make {(x^2 – 5xyy + y^2), (x^2 – 7xz + z^2), (y^2 – 11yz + z^2)} squares

$x^2 \; - \; 5 \,x \,y \; + \; y^2 \; = \; A^2$
$x^2 \; - \; 7 \,x \,z \; + \; z^2 \; = \; B^2$
$y^2 \; - \; 11 \,y \,z \; + \; z^2 \; = \; C^2$

Here are the first few solutions:

$\{ \, x, \; y, \; z, \; A, \; B, \; C \, \}$

$\{ \, 7, \; 35, \; 1, \; 7, \; 1, \; 29 \, \}$

$\{ \, 105, \; 517, \; 7, \; 83, \; 77, \; 477 \, \}$
$\{ \, 448, \; 2231, \; 56, \; 425, \; 168, \; 1899 \, \}$

$\{ \, 1173, \; 5809, \; 115, \; 1025, \; 667, \; 5139 \, \}$
$\{ \, 1885, \; 9353, \; 203, \; 1697, \; 957, \; 8163 \, \}$
$\{ \, 3003, \; 14935, \; 357, \; 2797, \; 1281, \; 12827 \, \}$
$\{ \, 4257, \; 21229, \; 559, \; 4115, \; 1333, \; 17901 \, \}$
$\{ \, 7424, \; 36735, \; 696, \; 6401, \; 4408, \; 32691 \, \}$
$\{ \, 8113, \; 40061, \; 671, \; 6755, \; 5307, \; 36189 \, \}$