If `x+z = 2y " and " b^2 = ac`, then prove that `a^(y-z)*b^(z-x)*c^(x-y) =1`.

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

If x : a = y : b = z : c , then prove that x^(3)/a^(2) + y^(3)/b^(2) + z^(3)/c^(2) = ((x+y+z)^(3))/((a+b+c)^(2))

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

a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove that 4z(x-y)(y-z)=y(x-z)^2 .

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

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

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

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)) .

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