If `(alpha,beta,gamma)!=(0,0,0)` is a solution of system of equations `x+y-z=0,x-2y+z=0,3x+6y-5z=0` then `(beta gamma)/(alpha^(2))=`

Solve the following system of homogeneous equations: x+y-z=0x-2y+z=03x+6y-5z=0

Find the solution of homogeneous system of equations: x-2y+z=0;x+y=z and 3x+6y=5z

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

Solve the following system of homogenous linear equations : x+y-z=0 , x-2y+z=0 , 3x+6y-5z=0

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

If alpha,beta,gamma are the roots of the equation x^(3)-px^(2)+qx-r=0 find the value of (beta+gamma)(gamma+alpha)(alpha+beta)

If alpha + beta + gamma = 2pi , then the system of equations x + (cos gamma)y + (cos beta)z = 0 (cos gamma) x + y + (cos alpha)z = 0 (cos beta )x + (cos alpha)y + z = 0 has :

If alpha,beta,gamma and delta are roots of equation x^(4)-7x^(2)+x-5=0, then the value of (alpha+beta+gamma)(alpha+beta+delta)(beta+gamma+delta)(alpha+gamma+delta) is equal to

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