Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x281+y29+z
225=1 Hint: By symmetry, you can restrict your attention to the first octant (where x,y,z≥0), and assume your volume has the form ????=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
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Let that be x
ATQ
Arrange accordingly to work backwards(Every thing is reversed)
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