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 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 the roots of the equation x^2 + 5x-49=0 , then find the value of cot(cot^-1 alpha + cot^-1 beta) .

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 and beta are the zeros of the quadratic polynomial p(y)=5y^2-7y+1 , find the value of 1/alpha+1/beta .

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

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

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

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