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 satisﬁed if and only if  xc  = r . As an alternate, you may prefer the following generalization . For real λ > 0, λ 6 = 1, consider the points x ∈ R k that satisfy  xa  = λ  xb  . Show that these points lie on a sphere. Part of this is to ﬁnd the center and radius of this sphere in terms of a , b and λ . What if λ = 1? [Last revised: September 18, 2010] 1...
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 Fall '10
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 Math, Inequalities, triangle, Complex number, Jerry L. Kazdan

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