If `alpha, beta` and `gamma` are the lengths of altitudes ABC and `Delta` be its area prove that :
`(1)/(alpha^(2))+(1)/(beta^(2)) + (1)/(gamma^(2)) = ((cot A + cot B + cot C))/(Delta)`

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

If alpha , beta , gamma are the roots of x^3 + 3x^2 -4x +2=0 then the equation whose roots are (1)/( alpha beta) ,(1)/( beta gamma) ,(1)/( gamma alpha) is

if alpha, beta, gamma are the roots of x^(3) + x^(2)+x + 9=0 , then find the equation whose roots are (alpha +1)/(alpha -1) , (beta+1)/(beta -1), (gamma+1)/(gamma -1)

If alpha, beta , gamma, delta are the roots of the equation x^4+x^2+1=0 then the equation whose roots are alpha^2, beta^2, gamma^2, delta^2 is

If alpha , beta , gamma are the roots of x^3 -3x +1=0 then the equation whose roots are alpha - (1)/( beta gamma) , beta - (1)/( gamma alpha ) , gamma - (1)/( alpha beta ) is

If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + r = n then the value of (alpha - 1/(beta gamma)) (beta -1/(gamma alpha)) (gamma-1/(alpha beta)) is:

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 , beta , gamma are the roots of x^3 + qx +r=0 then (1)/( alpha + beta - gamma) +(1)/( beta + gamma - alpha) +(1)/(gamma + alpha - beta) =

If alpha , beta , gamma are the roots of x^3 + qx +r=0 then (1)/( alpha + beta - gamma) +(1)/( beta + gamma - alpha) +(1)/(gamma + alpha - beta) =

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is: