Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid T² y² 22 + 4 81 16 + 1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y, z 20), and assume your volume has the form V = 8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: 9.

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