Question 1146973
(a + (a²+b³)^1/2)^(1/3) + (a - (a²+b³)^1/2)^(1/3)
<pre>
That is equivalent to:

{{{root(3,a + sqrt(a^2 + b^3)) + root(3,a - sqrt(a^2 + b^3))}}}

Cardano's cubic formula says that the solution to

{{{x^3+px+q=0}}} 

is 

{{{root(3,-q/2 + sqrt(q^2/4 + p^3/27)) + root(3,-q/2 - sqrt(q^2/4 + p^3/27))}}}

So if we set

a = -q/2 and b = p/3,

then

q = -2a and p = 3b

then

{{{root(3,a + sqrt(a^2 + b^3)) + root(3,a - sqrt(a^2 + b^3))}}}

is the solution to the cubic equation

{{{x^3+3bx-2a=0}}}

and therefore

{{{x^3+3bx=2a}}}

answer: 2a

Edwin</pre>