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Unformatted text preview: 5. Suppose a R k , b R k , and x R k . Find all c R k and r > 0 (depending on a and b) such that  xa  = 2  xb  is satised if and only if  xc  = r . As an alternate, you may prefer the following generalization . For real > 0, 6 = 1, consider the points x R k that satisfy  xa  =  xb  . Show that these points lie on a sphere. Part of this is to nd the center and radius of this sphere in terms of a , b and . What if = 1? [Last revised: September 18, 2010] 1...
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This note was uploaded on 03/06/2012 for the course MATH 508 taught by Professor Staff during the Fall '10 term at UPenn.
 Fall '10
 STAFF
 Math

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