SOLUTION: I need help help help ∀x, u ∈ R ∃α,β ∈ [0, 1] such that (αx+βu)^3=x^3+u^3 α,β??????????????

Question 765752: I need help help help

∀x, u ∈ R ∃α,β ∈ [0, 1] such that (αx+βu)^3=x^3+u^3
α,β??????????????
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
for convenience we use a=alpha, b=beta

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
:)
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SOLUTION: I need help help help ∀x, u ∈ R ∃α,β ∈ [0, 1] such that (αx+βu)^3=x^3+u^3 α,β??????????????