Question

If a^x = b^y = c^z and b² = ac, prove that y = `(2xz)/(z + x)`

Answer 1

Let a^x = b^y = c^z = k

⇒ `"a" = "k"^(1/x), "b" = "k"^(1/y), "c" = "k"^(1/2)`
It is also given that b² = ac
⇒ `"k"^(2/y) = "k"^(1/x) xx "k"^(1/2)`

⇒ `"k"^(2/y) = "k"^(1/x + 1/z)`

⇒ `(2)/y = (1)/x + (1)/z`

⇒ y = `(2zx)/(z + x)`.