need help in Kuhn tucker nonlinear analysis

[soul_]

Find the Max value of F(U)=u1^2+u2^2+u3^2 (and the values of ui to produce the maximum of F) subject to
u1-u2+u3=1
u1^2+u2^2<=2
u2^2+u3^2<=4

[If this is not clear please find the atttached document]

 

[_Eduardo_]

F(U) = u1^2+u2^2+u3^2 is the distance^2 to origin.

u1-u2+u3=1
u1^2+u2^2<=2
u2^2+u3^2<=4

Are the intersection of 2 ellipses (a 4th deg equation)==> the real solution more distant to the origin will be the maximum of F(U)

WolframAlpha said http://www.wolframalpha.com/input/?i=x-y%2Bz%3D1+and+x^2%2By^2%3D2+and+y^2%2Bz^2%3D4++

--> two real solutions:
U1 = [ -1.35731, -0.397133, 1.96017 ]
U2 = [ 0.675347, 1.24254, 1.56719 ]

but F(U1) > F(U2) then the solution is

U = [ -1.35731, -0.397133, 1.96017 ]
F(U) ~ 5.8422