Find the greatest value of `x^(2) y^(3) z^(4)` if `x^(2) + y^(2) + z^(2) = 1`, where x,y,z are positive.

Find the greatest value of x^2y^3z^4 if x^2+y^2+z^2=1,w h e r ex ,y ,z are positive.

Find the greatest value of x^2y^3z^4 if x^2+y^2+z^2=1,w h e r ex ,y ,z are positive.

If x+y+z=1 , then the minimum value of xy(x+y)^(2)+yz(y+z)^(2)+zx(z+x)^(2) is , where x,y,z inR^(+)

Find the value of 4x^2+y^2+25 z^2+4x y-10 y z-20 z x when x=4,y=3 and z=2.

Find the value of 4x^2+y^2+25 z^2+4x y-10 y z-20 z x when x=4,\ y=3 and z=2

If x+y -z = 4 and x^(2) + y^(2) + z^(2) = 30 , then find the value of xy- yz- zx

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

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

Find the values of x, y, z if the matrix A=[[0, 2y, z],[ x, y,-z],[ x,-y, z]] satisfy the equation A^(prime)A=I .

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .