`a=2,x=1,y=1,z=1 then a^xtimesa^ytimesa^z=`

If xyz=(1-x)(1-y)(1-z) Where 0<=x,y, z<=1 , then the minimum value of x(1-z)+y (1-x)+ z(1-y) is

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

If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"_1=|(1, 1, 1),(yz, z x,x y), (x, y, z)| , then prove that "Delta"+"Delta"_1=0 .

If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3dot

If a, b,c> 0 and x,y,z in RR then the determinant |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to:

If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^2+(z+1/z)^2>(100)/3

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+y^3+z^3

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

If the line (x-2)/-1=(y+2)/1=(z+k)/4 is one of the angle bisector of the lines x/1=y/-2=z/3 and x/-2=y/3=z/1 then the value of k is