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 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 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

Solve (2)/(sqrt(x))+(3)/(sqrt(y))=2 ;(4)/(sqrt(x))+(3)/(sqrt(y))=2

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

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x? (a)-1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) (c)-1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

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