2020 IMO Problems/Problem 2
Contents
[hide]Problem
The real numbers , , , are such that and . Prove that
Solution
Using Weighted AM-GM we get
So,
Now notice that
So, we get
Now, for equality we must have
In that case we get
~Shen Kislay kai
Video solution
https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems]
See Also
2020 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |