Math Problem Statement
cho 3 số dương a,b,c chứng minh rằng a^2/b + b^2/c +c^2/a lớn hơn hoặc bằng 3sqrt((a^4+b^4+c^4)/(a^2+b^2+c^2))
Solution
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Math Problem Analysis
Mathematical Concepts
Inequalities
Algebra
Cauchy-Schwarz Inequality
AM-GM Inequality
Formulas
a^2/b + b^2/c + c^2/a >= 3sqrt((a^4 + b^4 + c^4)/(a^2 + b^2 + c^2))
Cauchy-Schwarz: (a^2/b + b^2/c + c^2/a)(b + c + a) >= (a + b + c)^2
Theorems
Cauchy-Schwarz Inequality
AM-GM Inequality
Muirhead Inequality
Suitable Grade Level
Grades 11-12
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