If `3^x=9^y=27^(z)=729`, then show that `x+y+z=11`.

If a, b, c and x, y, z are positive, then show that (a/x + b/y + c/z) (x/a + y/b + z/c) ge 9

If (3x-5y)/5z+3y)=(x+5z)/(y-5x)=(y-z)/(x-z) then show that each ratio is x/y .

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If x/(3x-y-z) =y/(3y-z-x) =z/(3z-x-y) and x+y+z != 0 , then show that the value of each raio is equal to 1.

If x/(3x-y-z)=(y)/(3y-z-x)=(z)/(3z-x-y) and x+y+z=0 then show that the value of each of the ratio is equal to 1.

If (x)/(y+z-x)=(y)/(z+x-y)=(z)/(x+y-z) and x+y+z=0 then show that each ratio is equal to .

If 3 rational numbers x^(1//x) , y^(1//y) and z^(1//z) are equal and x^(yz)+y^(zx)+z^(xy)=729 , then find the value of x^(1//x)

If 3x+6y+9z=20/3, 6x+9y+3z=17/3 and 18x+27 y-z=113/9 , then what is the value of 75x+ 113y?