If α,β  are the roots of the equation 8x2−3x+27=0,  then the value of [(α2β)13+(β2α)13]  is

The given equation is 8x2−3x+27=0 ∴  sum of the roots : α+β=38, And product of the roots αβ=278     ∴  [(α2β)13+(β2α)13]=(α3αβ)13+(β3αβ)13                                                =((α3)13+(β3)13(αβ)13)                                        =α+β(αβ)1/3                                       =38(278)13=3832=14 .