Math Problem Statement
If x, y, z are distinct positive real numbers then find the range of {9(x²+y²)÷4z²}+{9(y²+z²)÷4x²}+{9(x²+z²)÷4y²}
Solution
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Math Problem Analysis
Mathematical Concepts
Inequalities
Symmetry in Algebra
Real Numbers
Formulas
S = 9(x² + y²)/4z² + 9(y² + z²)/4x² + 9(x² + z²)/4y²
AM-GM Inequality: x² + y² ≥ 2xy
Theorems
Arithmetic Mean-Geometric Mean (AM-GM) Inequality
Suitable Grade Level
Undergraduate Level