The sum of several positive numbers is equal to $10$, and the sum of their squares is greater than $20$. Prove that the sum of the cubes of these numbers is greater than $40$. (5 points)
Source: Spring 2005 Tournament of Towns Senior O-Level #5
Tags: algebra
The sum of several positive numbers is equal to $10$, and the sum of their squares is greater than $20$. Prove that the sum of the cubes of these numbers is greater than $40$. (5 points)