EXERCICE 1

ContourPlot3D[{x^2/4+y^2/9+z^2/25==1,z==x+y},{x,-5,5},{y,-5,5},{z,-5,5}]

S=FullSimplify[Solve[2x==2la*x/4-mu && 2y==2la*y/9-mu && 2z==2la*z/25+mu && x^2/4+y^2/9+z^2/25==1 && z==x+y,{x,y,z,la,mu}]]

f[x_,y_,z_]:=x^2+y^2+z^2

{f[x,y,z]/.S[[1]]//N,f[x,y,z]/.S[[2]]//N,f[x,y,z]/.S[[3]]//N,f[x,y,z]/.S[[4]]//N}

{5.118519836738659`,5.118519836738659`,13.88148016326134`,13.88148016326134`}

EXERCICE 2

ContourPlot[y^2-(x-1)^3==0,{x,0,4},{y,-5,5}]