Home
Class 12
MATHS
Using properties of determinants prove t...

Using properties of determinants prove that :
`{:|( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) |:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma ) `

Text Solution

Verified by Experts

The correct Answer is:
`x=2,y=3,z=5`
Promotional Banner

Similar Questions

Explore conceptually related problems

cos alpha sin (beta-gamma)+cos beta sin (gamma-alpha) +cos gamma(sin alpha-beta)=

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

If alpha+beta+gamma=2 pi, then

If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is

Let A and B denote the statement : A : cosalpha + cosbeta + cosgamma = 0 , B : sinalpha + sinbeta + singamma = 0 If cos(beta - gamma) + (gamma - alpha) + cos (alpha - beta) =-3/2 , then :

If cos ^(-1) alpha+cos ^(-1) beta+cos ^(-1) gamma=3 pi then alpha(beta+gamma)+beta(gamma+alpha)+gamma(alpha+beta)=

Let alpha, beta, gamma are distinct real numbers. The points with position vectors alpha i + beta j + gamma k , beta i + gamma j + alpha k , gamma i + alpha j + beta k

If A=[(alpha, beta),(gamma, -alpha)] is such that A^(2)=I , then

If a=cis alpha , b= cis beta , c= cis gamma and (a)/(b)+(b)/(c)+(c)/(a)=1 then cos (alpha-beta)+cos (beta-gamma)+cos (gamma-alpha)=

If alpha,beta,gammain(0,pi/2) , then (sin(alpha+beta+gamma))/(sinalpha+sinbeta+singamma) is :