If \( \Large a^{x} = b^{y} = c{z} \) and \( \Large \frac{b}{a} = \frac{c}{b} \) then \( \Large \frac{2z}{x + z} = ? \)
Correct Answer: A) \( \Large \frac{y}{x} \) |
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Description for Correct answer:
\( \Large \frac{b}{a} = \frac{c}{a} => b^{2} = ca \)
Again, \( \Large a^{x} = b^{y} = c^{z} = k \)
=> \( \Large a = k^{\frac{1}{x}}, b = k^{\frac{1}{y}} , c = k^{\frac{1}{z}} \)
\( \Large \therefore b^{2} = ac \)
=> \( \Large k ^{\frac{2}{y}} = k^{\frac{1}{x}} . k^{\frac{1}{z}} \)
=> \( \Large \frac{2}{y} = \frac{1}{x} + \frac{1}{z} = \frac{z + x}{zx} \)
=> \( \Large \frac{2z}{x + z} = \frac{y}{x} \)
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