MathDB

15

Part of 2015 Hanoi Open Mathematics Competitions

Problems(2)

max of 4(Σ a_i^3 )-(Σa_i^4) when Σa_i^2 <=8 (HOMC 2015 J Q15)

Source:

8/6/2019
Let the numbers a,b,ca, b,c satisfy the relation a2+b2+c2≤8a^2+b^2+c^2 \le 8. Determine the maximum value of M=4(a3+b3+c3)−(a4+b4+c4)M = 4(a^3 + b^3 + c^3) - (a^4 + b^4 + c^4)
maximuminequalitiesalgebra
max of 4(sum a_i^3 )-(sum a_i^4) when sum a_i^2 <=12 (HOMC 2015 S Q15)

Source:

9/7/2019
Let the numbers a,b,ca, b,c satisfy the relation a2+b2+c2+d2≤12a^2+b^2+c^2+d^2 \le 12. Determine the maximum value of M=4(a3+b3+c3+d3)−(a4+b4+c4+d4)M = 4(a^3 + b^3 + c^3+d^3) - (a^4 + b^4 + c^4+d^4)
algebramaximumSummationinequalities