Question

If a^x = b^y = c^z and b² = ac then y =
1. \(\frac{{xz}}{{x + y}}\)
2. \(\frac{{xz}}{{2\left( {x - y} \right)}}\)
3. \(\frac{{xz}}{{2\left( {z - x} \right)}}\)
4. \(\frac{{2xz}}{{z + x}}\)

Answer 1

Correct Answer - Option 4 : \(\frac{{2xz}}{{z + x}}\)

Calculation:

ax = by = cz and b2 = ac

Let ax = by = cz = k

⇒ a = k^1/x, b = k^1/y and c = k^1/z

b2 = ac

∴ k²/y = k1/y.k1/z

⇒ 2/y = 1/y + 1/z

⇒ y = 2xz/(x + z)