Math Problem Statement
a, b, c are positive numbers, prove that it is not possible for the inequalitiesa(1−b)>1/4,b(1−c)>1/4,c(1−a)>1/4, toholdatthesametime
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Inequalities
AM-GM Inequality
Quadratic Equations
Formulas
AM-GM inequality
Quadratic discriminant
Theorems
AM-GM inequality
Quadratic discriminant
Suitable Grade Level
Advanced High School
Related Recommendation
Prove the Inequality Involving Symmetric Radicals with a, b, c Satisfying (2a + b + c)(a + 2b + c)(a + b + 2c) = 64
Proving Inequality for Quadratic Functions Without Zeros
Inequality Proof: a^3/(a^2 + b^2) + b^3/(b^2 + c^2) + c^3/(c^2 + a^2) ≥ 1/2
Proving the Inequality a/b + b/a > 2 Using AM-GM
Inequality Proof with Cauchy-Schwarz for a^2/b + b^2/c + c^2/a