If `x+y+z=12a n dx^2+y^2+z^2=96a n d1/x+1/y+1/z=36 ,` then the value `x^3+y^3+z^3` divisible by prime number is________.

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/(z)= 36 . Then find the value 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 x, y, z in R are such that they satisfy x + y + z = 1 and tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(4) , then the value of |x^(3)+y^(3)+z^(3)-3| is

If x ,y ,a n dz are positive real umbers and x=(12-y z)/(y+z) . The maximum value of x y z equals.

The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+z^2-3x+3y+4z=8 is the same as the intersection of one of the spheres and the plane a. x-y-z=1 b. x-2y-z=1 c. x-y-2z=1 d. 2x-y-z=1

The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=z^2-3x+3y+4z=8 is the same as the intersection of one of the spheres and the plane a. x-y-z=1 b. x-2y-z=1 c. x-y-2z=1 d. 2x-y-z=1

If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a x2 3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |x_1y_1z_1x_2y_2z_2x_3y_3z_3|=(d-f){((d+2f))/(a b c)}^(1//2)

If x^2+9y^2+25 z^2=x y z((15)/x+5/y+3/z),t h e n x ,y ,a n dz are in H.P. b. 1/x ,1/y ,1/z are in A.P. c. x ,y ,z are in G.P. d. 1/a+1/d=1/b=1/c

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