kill(all)$

van = facebook.com/LearningCalculus$

f(x):= x^3 - 1/x^3 - 14$

s:solve(f(x),x)$

for i: 1 thru 6 do
(
    Sr:realpart(rectform(rhs(s[i]))),
    Si:imagpart(rectform(rhs(s[i]))),
    if(is(equal(Si,0))) then
        print("Answer ", "s[", i, "]: ",
            rectform(rhs(s[i])), " ~= ", bfloat(Sr))
)$

bfloat(1+sqrt(2));
bfloat((-4-(sqrt(2))/10)/10);

a:rectform(fullratsimp(rhs(s[3]-1/s[3])));

is(equal(a,2));

g(x):=x-1/x-2;