Difference between revisions of "2017 JBMO Problems/Problem 2"
(Created page with "== Problem == == Solution == == See also == {{JBMO box|year=2017|num-b=1|num-a=3|five=}}") |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | |||
| + | Let <math>x,y,z</math> be positive integers such that <math>x\neq y\neq z \neq x</math> .Prove that <cmath>(x+y+z)(xy+yz+zx-2)\geq 9xyz.</cmath> | ||
| + | When does the equality hold? | ||
== Solution == | == Solution == | ||
| Line 6: | Line 9: | ||
{{JBMO box|year=2017|num-b=1|num-a=3|five=}} | {{JBMO box|year=2017|num-b=1|num-a=3|five=}} | ||
| + | |||
| + | [[Category:Intermediate Algebra Problems]] | ||
be positive integers such that 
.Prove that ![\[(x+y+z)(xy+yz+zx-2)\geq 9xyz.\]](http://latex.artofproblemsolving.com/5/6/3/56366cbef963b44b24f2b97c3db0fc34d36dffab.png)
When does the equality hold?
