If `alpha,beta " are the roots of the equation "x^(2) - 2x - 1 =0, "then what is the value of " alpha^(2)beta^(-2)+alpha^(-2)beta^(2)`

If alpha and beta are the roots of the equations x^(2)-2x-1=0 , then what is the value of alpha^(2)beta^(-2)+beta^(2)alpha^(-2)

If alpha and beta are the roots of the equation x^(2) - 2x + 4 = 0 , then what is the value of alpha^(3) + beta^(3) ?

If alpha and beta are the roots of the equation x^(2)-x-1=0 , then what is (alpha^(2)+beta^(2))/((alpha^(2)-beta^(2))(alpha-beta)) equal to ?

If alpha,beta are roots of the equation x^(2)-px+q=0, then find the value of (i)alpha^(2)(alpha^(2)beta^(-1)-beta)+beta^(2)(beta^(2)alpha^(-1)-alpha)