[" (v) If "x=alpha+beta,y=alpha+beta w" and "z=alpha+beta w^(2)" ,then prove that,"],[x^(3)+y^(3)+z^(3)=3(alpha^(3)+beta^(3))]

If omega be a complex cube root of unity and x=alpha+beta,y=alpha+beta omega, z=alpha + beta omega^(2), show that, x^(3)+y^(3)+z^(3)=3(alpha^(3)+beta^(3)).

If x = a + b , y = a alpha + b beta , z = a beta + b alpha where alpha and beta are complex cube roots of unity , show that x^(3) +y^(3) + z^(3) = 3 (a^(3)+ b^(3))

IF alpha , beta are the roots of ax ^2 + bx +c=0 then (alpha ^3 + beta ^3)/(alpha ^(-3) + beta ^(-3)) =

If x = sin alpha, y = sin beta, z = sin (alpha + beta) then cos (alpha + beta) =

If alpha, beta are the roots of x^(2) + x + 3=0 then 5alpha+alpha^(4)+ alpha^(3)+ 3alpha^(2)+ 5beta+3=

If alpha,beta are the roots of x^(2)+x+3=0 then 5 alpha+alpha^(4)+alpha^(3)+3 alpha^(2)+5 beta+3=

If alpha, beta are the roots of x^(2) + x + 3=0 then 5alpha+alpha^(4)+ alpha^(3)+ 3alpha^(2)+ 5beta+3=

If =(beta-gamma)(alpha-delta),y=(gamma-alpha)(beta-delta),z=(alpha-beta)(gamma-delta) ,then value of x^(3)+y^(3)+z^(3)-3xyz is

If alpha,beta are the roots a^(x)-2bx+c=0 then alpha^(3)beta^(3)+alpha^(2)beta^(3)+beta^(2)alpha^(3)=