Let `alpha,beta,gamma,delta` be four real numbers such that `alpha^(2)+gamma^(2)=9` and `beta^(2)+delta^(2)=1` ,then the maximum value of `3(alpha beta-gamma delta)+4(alpha delta+beta gamma)` is

If alpha,beta,gamma,delta are four complex numbers such that (gamma)/(delta) is real and alpha delta-beta gamma!=0 then z=(alpha+beta t)/(gamma+delta t) represents a

Let alpha,beta,gamma and delta are four positive real numbers such that their product is unity,then the least value of (1+alpha)(1+beta)(1+gamma)(1+delta) is :

Let alpha , beta , gamma , delta be real numbers such that alpha^(2) +beta^(2) +gamma^(2) != 0 and alpha +gamma = 1 . Supose the point (3,2,-1) is the mirror image of the point (1,0,-1) with respect to the planet alphax + beta y + gammaz = delta . Then which of the following statements is/are TRUE ?

If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is

if alpha,beta the roots x^(2)+x+2=0 and gamma,delta the roots of x^(2)+3x+4=0 then find the value of (alpha+gamma)(alpha+delta)(beta+gamma)(beta+delta)

If cos(alpha+beta)sin(gamma+delta)=cos(alpha-beta)sin(gamma-delta) then the value of cot alpha cot beta cot gamma, is

Prove that: | alpha beta gamma alpha^(2)beta^(2)gamma^(2)beta+gamma gamma+alpha alpha+beta|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)