If `a^(x)=b^(y)=c^(z)` and `b^(2)=ac` prove that `(1)/(x)+(1)/(z)=(2)/(y)`

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

If a^(x)=b^(y)=c^(2) and b^(2)=ac, prove that y=(2xz)/(x+z)

If a^(x)=b,b^(y)=c and c^(z)=a, prove that xyz=1

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

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

if a,b,c are in G.P. and a^(x)=b^(y)=c^(z) prove that (1)/(x)+(1)/(z)=(2)/(y)

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

If x^(a) = y^(b) = z^ (c ) and y^(2) = xz, prove that b= ( 2ac)/( a+c)

If a/(y+z) = b/(z + x) = c/(x+y) , then prove that (a(b-c))/(y^(2)-z^(2)) = (b(c-a))/(z^(2)-x^(2)) = (c(a-b))/(x^(2)-y^(2)) .