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2023 SSMO Team Round Problems/Problem 6

Revision as of 22:25, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Suppose that <math>a,b,c</math> are positive reals satisfying<cmath>(a^3+4)(b^3+6)(c^3+8) = 8(a+b+c)^3.</cmath> Find the sum of all possible values of <math>\frac{...")
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Problem

Suppose that $a,b,c$ are positive reals satisfying\[(a^3+4)(b^3+6)(c^3+8) = 8(a+b+c)^3.\] Find the sum of all possible values of $\frac{bc}{a^2}.$ If you believe there are no solutions, put $0$ as your answer. If you believe the sum is infinity, put $1000$ as your answer.

Solution

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