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)`

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

If x,y,z are positive real numbers show that: sqrt(x^(-1)y)*sqrt(y^(-1)z)*sqrt(z^(-1)x)=1

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

If x ,y ,z are positive real number, then show that sqrt((x^(-1)y) x sqrt((y^(-1)z) x sqrt((z^(-1)x) =1

Assuming that x,y,z are positive real numbers,simplify each of the following: (sqrt(x^(-3)))^(5) (ii) (sqrt(x))^(-(2)/(3))sqrt(y^(4))-:sqrt(xy^(-(1)/(2)))

Find the least positive real number K such that for any positive real numbers x,y,z the following inequality holds x sqrt(y)+y sqrt(z)+z sqrt(x)<=K sqrt((x+y)(y+z)(z+x))

factorise 2x^(2)+y^(2)+8z^(2)-2sqrt(2)xy+4sqrt(2)yz-8xz