Hello to everybody. I'm totally desparate about a problem I'm trying to solve and can't. Could anybody help me?

I want tominimizethe quadratic function

$\displaystyle f(x,y,z)= \frac{1}{2}[(x-1)^{2}+(y-2)^{2}+(z-2)^{2}]$

under the constraints

$\displaystyle y=z$

$\displaystyle x^2+2y^2 \leq 1$

using the Kuhn-Tucker theorem... I'm troubled when I find a value of y that must be equal to z and I can't find the minimum...