If `alpha ,beta, gamma` are the parameters of points A,B,C on the circle `x^2+y^2=a^2` and if the triangle ABC is equilateral ,then

If alpha,beta, gamma are the lengths of altitudes of Delta ABC , then alpha^-2+ beta^-2+ gamma^-2 =

A plane meets the coordinate axes in points A,B,C and the centroid of the triangle ABC is (alpha,beta,gamma) , find the equation of the plane.

The roots z_(1),z_(2),z_(3) of the equation z^(3)+3 alpha z^(2)+3 beta z+gamma=0 correspond to the points A,B and C on the complex plane.Find the complex number representing the centroid of the triangle ABC, and show that the triangle is equilateral if alpha^(2)=beta

If alpha, beta , gamma are the lengths of the altitudes of Delta ABC , " then " alpha ^(-2) +beta ^(-2) +gamma^(-2) =

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:

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:

If alpha, beta, gamma are the roots of the equation x^(3) - 6x^(2) + 11x - 6 = 0 and if a = alpha^(2) + beta^(2) + gamma^(2) , b = alpha beta + beta gamma + gamma alpha and c = (alpha + beta) (beta + gamma)(gamma + alpha), then the correct inequality among the following is :

Find the equation of the plane, which meets the axes in A,B,C given that centroid of the triangle ABC is the point (alpha, beta, gamma) .