Question 765752
for convenience we use a=alpha, b=beta


{{{
(ax+bu)^3=(ax)^3+3(ax)^2(bu)+3(ax)(bu)^2+(bu)^3
}}}

so we need 


(ax)^3=x^3
(bu)^3=u^3

and

3(ax)^2(bu)+3(ax)(bu)^2=0

all are possible if a,b,x,u = 0

another solution is a=b=1, x=-u


I'm not positive, but I think this exhausts the real solutions

:)