If `A=B^x ,B =C^y` and `C=A^z` then `x:y:z =?`

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If x,y,z are in G.P and a^x=b^y=c^z ,then

If x = 10a, y = 3b , z = 7c and x : y : z = 10 : 3 : 7 , then (7x + 2y + 5z)/(8a + b + 3c) =

If a,b,c,d are in GP and a^x=b^y=c^z=d^u , then x ,y,z,u are in

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then prove that x/z+z/x=a/c+c/a

If a, b,c> 0 and x,y,z in RR then the determinant |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to:

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these