Let \mathcal{P} be a parallelepiped with side lengths x, y, and z. Suppose that the four space diagonals of \mathcal{P} have lengths 15,17,21, and 23. Compute x^{2}+y^{2}+z^{2}.
Let \mathcal{P} be a parallelepiped with side lengths x, y, and z. Suppose that the four space diagonals of \mathcal{P} have lengths 15,17,21, and 23. Compute x^{2}+y^{2}+z^{2}.