>>402
デカルトの葉線でござるか。与式から
1 = x^3 + y^3 + 1^3 - 3xy
　= (x+y+1)(xx+yy-xy-x-y+1),

f(x,y) = (x-1)^2 + (y-1)^2
　= {2(xx+yy-xy-x-y+1) + (x+y-2)^2}/3
　= {2/(x+y+1) + (x+y-2)^2}/3
　= {2/(s+1) + (s-2)^2}/3　　　(s=x+y)
　= (s^3 -3ss +6)/{3(s+1)},

df/ds = {2(s^3 -3s -3)}/{3(s+1)^2} = 0　より
　s = φ^(2/3) + φ^(-2/3) = 2.1038034　で最小
　{x,y} = {φ^(2/3), φ^(-2/3)},　　t = xy = 1,

　f(x,y) ≧ 2 - φ^(5/3) + φ^(-5/3) = 0.21838195
　φ = (1+√5)/2 = 1.618034