If `x=2alpha+1\ a n d\ y=alpha-1` is a solution of the equation `2x-3y+5=0` , find the value of `alpha`

If x = 2 - alpha and y = 2 + alpha is a solution of the equation 3x - 2y + 6 = 0, find the value of alpha . Find '3' more solutions of the equation.

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

If alpha, beta are the roots of the equation 5x^(2)-5x+1=0 , then find the value of (1)/(2)(a+b alpha+c alpha^(2)+d alpha^(3))+(1)/(2)(a+b beta+c beta^(2)+d beta^(3)) .

If alpha, beta be the roots of the quadratic equation 3x^(2)-6x+4=0 , find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alpha beta :

If alpha a n d beta are the roots of x^2-3x+2=0 find the value of (1+ alpha )(1+ beta ).

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If alpha,beta are the roots of the equation,x^(2)-2x+3=0, find the equation whose roots are alpha^(3)-3 alpha^(2)+5 alpha-1 and beta^(3)-beta^(2)+beta+5

If the roots of the quadratic equation 5x^2 - 2x - 3 = 0 be alpha and beta , find the value of (1)/(alpha)+(1)/(beta) .