Let x,y and z be real numbers such that x+y+z=20 and x+2y+3z=16 .What is the value of x+3y+5z?

Let A=[(x,y,z),(y,z,x),(z,x,y)] , where x, y and z are real numbers such that x + y + z > 0 and xyz = 2 . If A^(2) = I_(3) , then the value of x^(3)+y^(3)+z^(3) is__________.

If x,y and z are three real numbers such that x+y+z=4 and x^(2)+y^(2)+z^(2)=6, then show that each of x,y and z lie in the closed interval [(2)/(3),2]

Let x, y, z be non-zero real numbers such that x/y + y/z + z/x = 7 and y/x + z/y + x/z = 9 , then (x^3)/y^3 + y^3/z^3 + z^3/x^3 - 3 is equal to

Let x,y,z are positive real numbers satisfying x+y+z=1 . If the maximum value of x^(3)y^(2)z can be expressed as (a)/(b) where a and b are co-prime,then the value of (a+b) is

Let x,y,z be positive real numbers such that x+y+z=12 and x^(3)y^(4)z^(5)=(0.1)(600)^(3) Then x^(3)+y^(3)+z^(3) is