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.

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

Given that x,y,z are positive real numbers such that xyz=32 , the minimum value of sqrt((x+2y)^(2)+2z^(2)-15) is equal to

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

If y z+z x+x y=12 ,w h e r ex ,y ,z are positive values, find the greatest value of x y zdot

If x,y,z be three positive numbers such that xyz^(2) has the greatest value (1)/(64) , then the value of (1)/(x)+(1)/(y)+(1)/(z) is

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x y ,t h e nu is always a. non-negative b. zero c. non-positive d. none of these

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z