MathDB

1

Part of 2017 Austria Beginners' Competition

Problems(1)

inequality

Source: 48th Austrian Mathematical Olympiad Beginners' Competition(2017)

2/27/2018
The nonnegative real numbers aa and bb satisfy a+b=1a + b = 1. Prove that:
12≤a3+b3a2+b2≤1\frac{1}{2} \leq \frac{a^3+b^3}{a^2+b^2} \leq 1
When do we have equality in the right inequality and when in the left inequality?
Proposed by Walther Janous
inequalitiesalgebraAustria