Difference between revisions of "2000 IMO Problems/Problem 2"
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Let <math>a, b, c</math> be positive real numbers with <math>abc=1</math>. Show that | Let <math>a, b, c</math> be positive real numbers with <math>abc=1</math>. Show that | ||
| − | <cmath>\left( a-1+\frac{1}{b} \right)\left( b-1+\frac{1}{c} \right)\left( c-1+\frac{1}{a} \right) le 1</cmath> | + | <cmath>\left( a-1+\frac{1}{b} \right)\left( b-1+\frac{1}{c} \right)\left( c-1+\frac{1}{a} \right) \le 1</cmath> |
==Solution== | ==Solution== | ||
be positive real numbers with 
. Show that
![\[\left( a-1+\frac{1}{b} \right)\left( b-1+\frac{1}{c} \right)\left( c-1+\frac{1}{a} \right) \le 1\]](http://latex.artofproblemsolving.com/e/9/6/e96e8028ff8719b9a661de10c0cb70fc7b43ca67.png)
