Difference between revisions of "2017 JBMO Problems/Problem 2"
Numbercrunch (talk | contribs) (→Solution) |
(→Solution) |
||
Line 12: | Line 12: | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
Hence <cmath>(x+y+z)(xy+yz+xz-2)\geq 9(z)(z+1)(z+2)</cmath> | Hence <cmath>(x+y+z)(xy+yz+xz-2)\geq 9(z)(z+1)(z+2)</cmath> | ||
+ | |||
+ | == Solution 2 == | ||
+ | Expanding the equation gives | ||
+ | <cmath>x^2y + x^2z + y^2x+ y^2z + z^2x + z^2y</cmath> | ||
== See also == | == See also == |
Revision as of 11:07, 22 July 2021
Contents
[hide]Problem
Let be positive integers such that .Prove that When does the equality hold?
Solution
Since the equation is symmetric and are distinct integers WLOG we can assume that . Hence
Solution 2
Expanding the equation gives
See also
2017 JBMO (Problems • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |