A) \[\frac{xz}{x+z}\]
B) \[\frac{xz}{2(x-z)}\]
C) \[\frac{xz}{2\,\,(z-x)}\]
D) \[\frac{2xz}{(x+z)}\]
Correct Answer: D
Solution :
\[{{a}^{x}}={{b}^{y}}={{c}^{z}}=k\] \[a={{k}^{\frac{1}{x}}},\] \[b={{k}^{\frac{1}{y}}},\] \[c={{k}^{\frac{1}{z}}},\] \[{{b}^{2}}=ac\] \[\Rightarrow \] \[{{({{k}^{\frac{1}{y}}})}^{2}}={{k}^{\frac{1}{x}}}.{{k}^{\frac{1}{z}}}\] \[\Rightarrow \] \[{{k}^{\frac{2}{y}}}={{k}^{\frac{1}{x}}}+{{k}^{\frac{1}{z}}}\] \[\therefore \] \[\frac{2}{y}=\frac{1}{x}+\frac{1}{z}\] \[\Rightarrow \] \[y=\frac{2xz}{x+z}\]
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