1961 IMO Problems/Problem 2
Revision as of 10:36, 28 December 2007 by Johan.gunardi (talk | contribs)
Problem
Let , , and be the lengths of a triangle whose area is S. Prove that
In what case does equality hold?
Solution
Substitute , where
This shows that the inequality is equivalent to $a^2b^2+b^2c^2+c^2a^2\lea^4+b^4+c^4$ (Error compiling LaTeX. Unknown error_msg).
This can be proven because . The equality holds when , or when the triangle is equilateral.
1961 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |