" If "x+z=2y" and "b^(2)=ac," then let us show that "a^(y-z)b^(z-x)c^(x-y)=1

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)=ac, then show that y=(2zx)/(z+x)

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

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 aY+z)=b(z+x)=c(x+y) and out of a,b,c no two of them are equal then show that, (y-z)/(a(b-c))=(z-x)/(b(c-a))(x-y)/(c(a-b))

If x^(2) : (by + cz) =y^(2) : (cz + ax) = z^(2) : (ax + by) = 1 , then show that a/(a+x) + b/(b+y) + c/(c+z) = 1 .

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

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