Question

1/alpha root 2 +1/beta square v)alpha cube+beta cube

Answer 1

We can write,

(α+β)^3 = (α+β)*(α+β)*(α+β)

= (α+β)*(α^2+2αβ+β^2)

= α^3+β^3+3αβ(α+β)

=>

(α+β)^3 -3αβ(α+β) = α^3+β^3

(α+β){(α+β)^2 -3αβ} = α^3+β^3

(α+β)(α^2+β^2+2αβ-3αβ) = α^3+β^3

(α+β)(α^2+β^2-αβ) = α^3+β^3

=>

α^3+β^3 = (α+β)(α^2+β^2-αβ)