alleryIf a^x = b^y = c^z and b^2 = ac, then 1/x + 1/z equals
A2/y
B1/y
C2y
Dy
Answer & Solution
Correct answer: A. 2/y
1. Let a^x = b^y = c^z = k; then a = k^(1/x), b = k^(1/y), c = k^(1/z).
2. Given b^2 = ac, substitute: k^(2/y) = k^(1/x) * k^(1/z) = k^(1/x + 1/z).
3. Equating exponents: 2/y = 1/x + 1/z.
4. So 1/x + 1/z = 2/y.
_Source: ICAI BoS Foundation Paper 3, Ch 1 Unit III 'Indices', p.14_
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