Question: Minimize?

question1:

with(Optimization)

Minimize((1-b^2)/a+(1-c^2)/b+(1-a^2)/c, {a^2+b^2+c^2 = 1}, assume = nonnegative)

the result is strange:

[3.46410161513774462, [a = .577350269189626620, b = .577350269189626620, c = .577350269189626620]]

make the datatype not the float form in the results. 3.4641... to 2 sqrt(3)

question2:how to do this.I use sqrt(1-a^2-b^2) to substitute for c.

Minimize((1-b^2)/a+(1-a^2)/sqrt(1-a^2-b^2)+(a^2+b^2)/b, assume = nonnegative)

question3:

the result in question1 is not like that generated in Mathematica

g[a_, b_, c_] := (1 - b^2)/a + (1 - c^2)/b + (1 - a^2)/c

Minimize[{g[a, b, c],
  a^2 + b^2 + c^2 == 1 && a > 0 && b > 0 && c > 0}, {a, b, c}]

{2 Sqrt[3], {a -> 1/2, b -> 7/16, c -> Sqrt[143]/16}}

question4:

Mathematica can't minimize this:

f[a_, b_] = (1 - b^2)/a + (1 - c^2)/b + (1 - a^2)/c /.
  c -> Sqrt[1 - a^2 - b^2]=(1 - b^2)/a + (1 - a^2)/Sqrt[1 - a^2 - b^2] + (a^2 + b^2)/b

Minimize[{f[a, b], a > 0 && b > 0}, {a, b}]