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Homework Statement
Suppose [itex] a \in R^{k},b \in R^{k}[/itex]. Find [itex] c \in R^{k}[/itex] and [itex] r > 0[/itex] such that
|x-a| = 2|x-b|
if and only if |x-c| = r.
Homework Equations
Solution:
3c = 4b - a, 3r = 2|b-a|
The Attempt at a Solution
Technically, I can't seem to find any way to express |x-c| in terms of |x-a| or |x-b| except using the triangle inequality.
The idea of the exercise is a complete mystery to me. What is the use of proving this theorem?
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