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 :
Let \[{{a}^{x}}={{b}^{y}}={{c}^{z}}=k\] Then, \[a={{k}^{\frac{1}{x}}},\,\,b={{k}^{\frac{1}{y}}},\,\,c={{k}^{\frac{1}{z}}};\,\,{{b}^{2}}=ac\] \[\Rightarrow \] \[\,{{\left( {{k}^{\frac{1}{y}}} \right)}^{2}}={{k}^{\frac{1}{x}}}\times {{k}^{\frac{1}{z}}}\] \[\Rightarrow \] \[\,\frac{2}{y}=\frac{1}{x}+\frac{1}{z}=\frac{x+z}{xz}\] \[\Rightarrow \] \[y=\frac{2xz}{\left( x+z \right)}\]
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