Question

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

Answer 1

Let ax = by = cz = k

∴ a = `k^(1/x) ; b = k^(1/y) ; c = k^(1/z)`

Also, We have b² = ac 

∴ `( k^(1/y))^2 = ( k^(1/x)) xx ( k^(1/z))` 

⇒ `k^(2/y) = k^( 1/x + 1/z )`

⇒ `k^(2/y) = k^[ z + x ]/[  xz ]`

Comparing the powers we have

`2/y = [ z + x ]/[ xz ]`

⇒ `y = [ 2 xz ]/[ z + x ]`