If 2ˣ = 5ʸ = (10)⁻ᶻ, then 1/x + 1/y + 1/z =यदि 2ˣ = 5ʸ = (10)⁻ᶻ, तो 1/x + 1/y + 1/z =

1. A7/32
2. B0
3. C7/16
4. D7/48

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Correct answer: B. 0

Explanation

Let 2ˣ = 5ʸ = 10⁻ᶻ = k. Then 2 = k^(1/x), 5 = k^(1/y) and 10 = k^(−1/z). Since 2 × 5 = 10, k^(1/x + 1/y) = k^(−1/z), so 1/x + 1/y = −1/z. Hence 1/x + 1/y + 1/z = 0.माना 2ˣ = 5ʸ = 10⁻ᶻ = k। तब 2 = k^(1/x), 5 = k^(1/y) और 10 = k^(−1/z)। चूँकि 2 × 5 = 10, k^(1/x + 1/y) = k^(−1/z), अतः 1/x + 1/y = −1/z। इसलिए 1/x + 1/y + 1/z = 0।