If, for positive real numbers x, y, z, the numbers `x+y,` 2y and y + z are in harmonic progression, then which one of the following is correct ?

Let x, y, z be positive real numbers such that x, y, z are in GP and tan^(-1)y" and "tan^(-1)z are in AP. Then which one of the following is correct?

If x/(y+z) = y/(z+x) = z/(x+y) then which one of the following is correct ?

If x and y are real numbers such that x gt y and |x| gt |y| ,then which one of the following is correct ?

If x, y, z are positive real numbers such that x+y+z=a, then

If x, y, z are positive real numbers such that x+y+z=a, then

If |(y,x,y+z),(z,y,x+y),(x,z,z+x)|=0 , then which one of the following is correct ?

If |{:(y,x,y+z),(z,y,x+y),(x,z,z+x):}|=0 , then which one of the following is correct ?

Let x,y,z be positive reals , which of the which following imples x=y=z?

Three positive distinct numbers x, y, z are three terms of geometric progression in an order and the numbers x + y, y + z, z + x are three terms of arithmetic progression in that order. Prove that x^x . y^y = x^y . Y^z . Z^x .