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(D) Given the equation of the sphere: $2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z = 1$.Dividing by $2$,we get: $x^2 + y^2 + z^2 - 3x + y - 2z = \frac{1}{2}$.Th

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$2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z - 25 = 0$

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(D) Given the equation of the sphere: $2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z = 1$.Dividing by $2$,we get: $x^2 + y^2 + z^2 - 3x + y - 2z = \frac{1}{2}$.The center of the sphere is $C = (\frac{3}{2}, -\frac{1}{2}, 1)$.The radius $r$ is given by $\sqrt{g^2 + f^2 + h^2 - d} = \sqrt{(\frac{3}{2})^2 + (-\frac{1}{2})^2 + (1)^2 - (-\frac{1}{2})} = \sqrt{\frac{9}{4} + \frac{1}{4} + 1 + \frac{1}{2}} = \sqrt{\frac{16}{4}} = 2$.The required sphere is concentric,so its center is also $(\frac{3}{2}, -\frac{1}{2}, 1)$.The radius of the required sphere is $R = 2 	imes r = 2 	imes 2 = 4$.The equation of the required sphere is $(x - \frac{3}{2})^2 + (y + \frac{1}{2})^2 + (z - 1)^2 = 4^2$.Expanding this: $x^2 - 3x + \frac{9}{4} + y^2 + y + \frac{1}{4} + z^2 - 2z + 1 = 16$.$x^2 + y^2 + z^2 - 3x + y - 2z + \frac{14}{4} = 16$.$x^2 + y^2 + z^2 - 3x + y - 2z + 3.5 - 16 = 0$.$x^2 + y^2 + z^2 - 3x + y - 2z - 12.5 = 0$.Multiplying by $2$: $2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z - 25 = 0$.

The equation of the sphere concentric with the sphere $2x^2 + 2y^2 + 2z^2 - 6x + 2y - 4z = 1$ and having double its radius is:

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