Y by
Real numbers
satisfy the following conditions:
and
What are the possible values of the expression
![\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{a}?
\]](//latex.artofproblemsolving.com/6/7/8/6784020530976c4d63dfb33071960cdffba6d056.png)
Proposed by Vadym Solomka

![\[
1000 < |a| < 2000, \quad 1000 < |b| < 2000, \quad 1000 < |c| < 2000,
\]](http://latex.artofproblemsolving.com/1/7/6/17678804f32f7ef07883069c600fe925215a46b8.png)
![\[
\frac{ab^2}{a+b} + \frac{bc^2}{b+c} + \frac{ca^2}{c+a} = 0.
\]](http://latex.artofproblemsolving.com/0/3/f/03f2e66184e7e7593275c1febc48979b06cea1db.png)
![\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{a}?
\]](http://latex.artofproblemsolving.com/6/7/8/6784020530976c4d63dfb33071960cdffba6d056.png)
Proposed by Vadym Solomka
We have your learning goals covered with Spring and Summer courses available. Enroll today!
Something appears to not have loaded correctly.