Expressing output voltage in a circuit with zener diodes without any value given
I do not want to simply provide the solution, but I can point you in the right starting direction. 

I am assuming that you have already seen the fundamentals of an Inverting Op-Amp:


  Inverting Op-Amp Fundamental Properties
  


Your circuit is of the same nature, but has a complex feedback resistor \$R_{f}\$.
Since you mentioned that these are ideal zener diodes, we can ignore their resistance, and only need to pay attention to the conditions when they are conducting current.  

If at least one zener is not conducting, then the effective \$R_{f}\$ is equal to your \$R_{2}\$.
If both zeners are conducting, then the effective \$R_{f}\$ is equal to \$R_{2}\parallel\$\$R_{3}\$.  

The final piece of the puzzle is to identify what circuit scenario is required in order for both zener's to conduct.  

Each Zener will conduct current when either:
 - The forward voltage is more positive than its Zener Forward Voltage (\$V_{F}\$)
 - The reverse voltage more negative than its Zener_Breakdown_Voltage (\$V_{Z}\$)
(Fundamentals of Zener Diodes)  

There are two scenarios when both Zeners are conducting:
- Scenario 1: (\$V_{ZD1}\geq\$ \$V_{F\_ZD1}\$) &amp;&amp; (\$V_{ZD2}\leq\$ \$V_{Z\_ZD2}\$)
- Scenario 2: (\$V_{ZD1}\leq\$ \$V_{Z\_ZD1}\$) &amp;&amp; (\$V_{ZD2}\geq\$ \$V_{F\_ZD2}\$)  

Thus, the resulting \$u_{o}(u_{i})\$ will be comprised of two discrete equations:
- One equation for the voltage states where \$R_{f}\$ == \$R_{2}\$
- One equation for the voltage states where both zeners to be conducting