The Answer Is Not 3

Algebra Level 5

Consider all ordered triples of positive real numbers (a,b,c) (a, b, c) such that a2+b2+c2=52(ab+bc+ca). a^2 + b^2 + c^2 = \frac{5}{2} (ab + bc + ca ) . To 3 decimal places, what is the minimum value of

a+b+cabc3? \frac { a+b+c} { \sqrt[3]{abc} } ?

It should be clear that a=b=c a = b = c doesn't satisfy the given condition, which is why the answer is not 3.
You will likely need to use a calculator to evaluate the final expression.


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