If `x,y,x gt 0 and x+y+z=1` then `(xyz)/((1-x) (1-y) (1-z))` is necessarily.

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x,y,z are in G.P. (x,y,z gt 1) , then (1)/(2x+log_(e)x) , (1)/(4x+log_(e)y) , (1)/(6x+log_(ez)z) are in

Verify that x3+y3+z3-3xyz=1/2(x+y+z)[(x-y)2+(y-z)2+(z-x)2]

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y+z is also equal to 1/x+1/y+1/z (b) x y z x y+y z+z x (d) none of these

If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y+z is also equal to 1/x+1/y+1/z (b) x y z x y+y z+z x (d) none of these

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