For positive reals a,b,c with √a+√b+√c≥3 prove that a3a2+b+b3b2+c+c3c2+a≥32
Problem
Source: Kazakhstan Junior National Olympiad , i e 9 grade, problem 5
Tags: inequalities, Kazakhstan 2022, inequalities proposed, algebra
Source: Kazakhstan Junior National Olympiad , i e 9 grade, problem 5
Tags: inequalities, Kazakhstan 2022, inequalities proposed, algebra
For positive reals a,b,c with √a+√b+√c≥3 prove that a3a2+b+b3b2+c+c3c2+a≥32