The minimum value of `x^(2)+y^(2)+z^(2) " if " ax+by+cz=p`, is :

The minimum value of y=5x^(2)-2x+1 is

The minimum value of |2z-1|+|3z-2| is

If x,y,z are variables and 3tan x+4tany+5tanz=20, then the minimum value of tan^(2)x+tan^(2)y+tan^(2)z, is

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^(+)

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.

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

If ax+by+cz = p , then minimum value of x^2 + y^2 + z^2 is

If a x+b y+c z=p , then minimum value of x^2+y^2+z^2 is (p/(a+b+c))^2 (b) (p^2)/(a^2+b^2+c^2) (a^2+b^2+c^2)/(p^2) (d) ((a+b+c)/p)^2

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

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