The Answer Is Not 3
Algebra
Level
5
Consider all ordered triples of positive real numbers \( (a, b, c) \) such that \[ a^2 + b^2 + c^2 = \frac{5}{2} (ab + bc + ca ) .\] To 3 decimal places, what is the minimum value of
\[ \frac { a+b+c} { \sqrt[3]{abc} } ? \]
It should be clear that \( a = b = c \) 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.
by
Calvin Lin