Calculus 3: Find the distance between the spheres?

Posted on 2017-04-26 18:25:00 in Math by NICOLE

Find the distance between the spheres x^2 y^2 z^2 = 4 and x^2 y^2 z^2 = 4x 4y 4z - 11 

Maybe its just been a long day, but im confused. 

First, rewrite the 2nd equation into standard form 
(x^2 -4x (-2)^2) (y^2 -4y (-2)^2) (z^2 -4z (-2)^2) = -11 3(-2)^2 
(x-2)^2 (y-2)^2 (z-2)^2 = 1 

So the center of the first sphere is at origin, with radius 2. And the second sphere is centered at (2,2,2) with radius 1. 

What do i do from here? I had initially thought the spheres were touching given that sphere 1 has radius 2 and sphere 2 is centered at (2,2,2), but apparently i err. The answer is given as 2 * sqrt(3) -3 

Maybe im just cant add or do algebra?

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