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 (log)_(10)(x^3+y^3)-(log)_(10)(x^2+y^2-x y)lt=2,w h e r ex ,y are positive real number, then find the maximum value of x ydot

If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r ex ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

If x+y+z=5 and x y+y z+z x=3 , then the greatest value of (x) is

Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz are not all zero, then the value of a b+b c+c a is 0 b. 1 c. -1"" d. none of these

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

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.

Let x ,y ,z in R such that x+y+z=6a nd x y+y z+z x=7. Then find the range of values of x ,y ,a n dzdot

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

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

The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a. -1 b. 0 c. 1 d. none of these